One of the major incontinences of cycling is flat break downs. Sudden and dramatic is a sign of a picked up piece of glass, tax, OR a sliver of wire debris. These type of flats are easy fixed. The most frustrating problem is a developing trend of a persistent going down tire that are hard to find the cause unless you know what to look for.
Budget bikes tend to be fitted with budget tires that tend to pick up a collection of tiny fragments embedding themselves in the tire. Depending on your luck, they can remain there for weeks without a problem, notorious for puncturing the inner tube at a latter date. To keep costs down the tire manufactures had taken short cuts with the tire quality. These haven't anti-puncture technology expensive bikes are fitted with.
Examining the circumference sometimes we came across evidence we ran over tar or sticky gum that stuck a glob of tiny stones and glass fragments. The most frustrating challenge is a recognizance of the circumference reveling nothing that seems to be puncturing the inner tube.
It is likely a hidden piece of glass ( or stone ) pushed deeply hidden out of sight in the fabric of the tire, where it can be overlooked. Hidden bodies left in the tire will keep puncturing the inner tube, time and time again. These have to be found and removed.
I don't have to remind you of the dangers of picking out with a sharp poker while the tire inflated with tragic results. It is best done vacuum flat. A needle point poker is ideal getting at the tiny fragment. Blunt instruments tend to push the offending object deeper into the tire trying in a tempt to lever it out.
The wheel removed, tire off, and the inner tube out, turning your attention to inside of the tire can be reveling. The inside fabric is good contrast allowing easer spotting. Go round carefully looking for a hidden fragment.
Once found, it is a simple mater of pushing out from the inside ideal avoiding the risk of probe lever damage leveraging from the outside.
Repairing inner tubes with patch failures is often frustrating. It is often the cause by cements not taking, a sign the surface of the tube was not properly prepared. Tires that won't  stay tight constantly softening, is either the latter or an over looked object still embedded in the in the tire.
Patches tend to hold fast compressing dips in the inner tube at that point. Tires don't even out the tube pressures leaving uneven pressure on the tire. The patch is a week pressure point where the rest of the tube takes the pressure resulting in uneven inner tube pressure transferred to the tire.
Tire rims that look like the are not seat properly on the steel rim have been damaged. Observing the tire rim seating of new and good bikes is a good guide of what things should be. The tire rim is a perfect circle running parallel with the entire circumference of the steel rim in perfect symmetry.
Damaged tire rims have an distorted oval run round the steel rim. The tire rim can look as if it is not going to hold on for long in some places. Severe damage is likely caused by someone forcing a tight tire off the steel rim with damaging levers ripping and tearing at the steel wire of the tire's rim. Things are made worse by uneven inner tube pressures.
Rider weight compresses soft tires and inner tubes. If an uneven inner tube pressure stresses the walls of the tire rim bulge points. There will be potential further tire wall damage being done to the already week tire rim bulge.
New and good inner tubes evenly distribute the pressure firmly and  evenly keeping the walls of the tires full. Hard and full not only make bikes feel solid and sturdy on the road, but also reduces road paddle resistance.
Constantly swapping with different tires, can lead to these kind of tire problems. The next time you have the tire off ( or access to any bicycle rim ) observe the inside edges of the tire and wheel rims. Most of us are unaware there is either a hooked or flat on the edge to bicycle rims. Correspondingly there should be a matching hook or flat design in the rim of the tire too.
Looking at tire rims you will find 2 types a hook or a flat edge. If you assemble a hooked tire on a flat edged rim the tire doesn't sit properly. There will be tire damage issues transferred to the inner tube too as well. So too, a flat edge tire rim assembled on a hooked rim. Hook or flat rims need proper corresponding hooked or flat rim edge matting.
Other causes ignoring arrows pointing in the drive direction when refitting. Pointing the opposite drive direction for both rear and front wheel, there will be tire damage issues transferred to the inner tube as well.
Bikes are best upside down resting on the seat and handle bars turning the wheel. Observe if there is any arrow on the tire wall. Turning the wheel in the drive direction note the arrow pointing direction. At this point you can check round the circumference of the tire to see if an offending object can found out side the tire assessment.
Having a good inner tube on hand will get you going as quickly the time it takes to replace it. Otherwise salvaged with a patchy reaper kit. If at a petrol station you're lucky with the handy free air pump station.
If on the side of the road you will need a hand pump. Pumping up the inner tube will reveal If a previous patch is leaking. Inflating the inner tube you will soon feel a column of air from the patch or an expanded hole air leak giving itself away. If a leaking patch is not holding fast any more.
A sign of leaking patches the surface of the inner tube wasn't properly prepared that can easily be ripped off. Patches that can't is the way they should be. Properly prepared inner tube surface you should never be able to tear off. If it does is your flatting source you can to tear off and start over.
If you don't clean off the reaming cement residue the patch will always have the same problem.
Tearing off there will be mess of reaming cement left. Appling new cement straight over it is the cause patch repair failure. This residue must be cleaned off.
Using fine engineering emery paper just won't cut it with out a lot of time and effort. To fine and time consuming. You will need coarse carpenter's sand pepper or the the cheese grater scraper provided in your patchy kit. If you don't scrape off the remaining comment the new cement will never hold. Scrape all of it away the whole area the new patch.
If there is no previous patch or the patch is OK, pin holes in inner tubes are notorious to find as an offending body hiding in the tire. Pin holes are caused by hidden offending objects in the tire. To find pin holes you need inflate expanding the inner tube. Pin holes are so tiny they can be extremely difficult to tell any column of air anywhere in the tube.
Hand pumping air can leak out faster than you can put in constantly loosing expanding pressure expanding the pin hole.
If a patch is not a concern you can pay attention on finding the hole in the tube with the pump. In the case of a budget hand pumps making no headway, depending whether you are left or right handed, you may need to stretch out the rubber of the as you pump to encourage the pin whole tio expand.
When you feel a column of air you have located the hole. Pin holes are extremely easy to loose site of. So it is prudent while you have the chance stretch the rubber so is manageable. Relocating pin is just as difficult to find again. You can apply a marking spot with a ball point pen. Circle the hole.
Prepare the surface of the inner tube with cause carpenters sand paper or the cheese grater like scrapper provided with the patchy kit. If you don't scrape a cause clean area round the hole the size of the patch, the cement won't hold, otherwise another patch repair failure.
If you don't scrape an area the size of the patch you're using the edges will be week where they are always the week points of any patch. As you scrape you will observe it often helps hide the hole. This is where the pen circle cones in handy before you started scrapping.
The scrapping done properly patches are pretty sturdy standing up the rigors of high tire pressure for a long time. However, in a sense patched inner tubes are weakened for rear wheels specially high tier pressure when using your carrying stuff a donkey.
This is because the rear wheel is taking all the weight on the rear. Patched rear wheel tubes  should be swapped with good front wheel tubes. It is recommended policy with week tires.
If you're using a brand new kit, unscrew the cap. In the top is a little pin. Turn over and pierce the silver seal. Don't empty the container or you will end up a messy glob. Don't squeeze it. Let a drop out to a small glob right on the whole. Replace the cap.
Stretch the hole wide to let some of the cement drain into it and let close to help the cement plug it. When spreading the cement larger than the large patch make sure you keep the cement clean or particles, grease and dirt contaminates the cement. Even dry clean fingers still can leave residue oily finger grease. Be careful with seating on hot summer days.
Make sure you allow the cement to dry sticky covering well the area of the patch. As you apply the cement you will observe it tends to hide the hole. Patches stick best when applied when the cement is tacky. Now you can tear off the silver backing of the patch.
It is not really necessary, but a helpful option to spread some cement on the underside of the patch itself spreading to the edges to insure you have covered your bases. Let dry tacky.
You will observe spreading the cement hides the hole. Eye up the best you can a line of site the center of the pen circle marker ( or the hole itself, if you can see it ) to the center of the patch and press on. You will only have one shot the cement hiding the hole, as the cement will stick fast immediately. Watch your eye angle coordination on the hidden hole squares the patch exactly centering it in the center of the patch.
Use any round edge pressing down the edges. Don't concentrate so much on the center but round the edges of the patch.
If you have a spare inner tube, that is beyond reaper you can use it as a shoe inside the tire. Cut off the valve. A patch can be used to cover the gapping hole. The spare helps to act as a buffer shoe between the inside roof of the tire and the ball of the inner tube the tire rides on.
Before you reassemble the tire don't forget about any direction of the drive arrow on the tire wall must correspond with the crank drive direction. Now the inner tube can be reassembled back into the tire and fit the tire the arrow pointing in the direction of free wheel or sprocket crank push direction.
You may have experienced a tight getting off or on tight tire. A proper scrapping the patch will be sturdy enough to pump up to the maximum tire pressure recommended on the tire wall of the tire. Pumped up to the maximum recommended tire pressure we feel a sturdy solid and easier ride.  Fitting an extra shoe might be difficult to get the tire back on tough.
Other than that, an expense inner tube has a extra thick hide making them puncture resistant. Expensive tires essentially the same lining the inside. The anti puncture compound built into expensive tires  is what makes them more expensive.