Dryers do require some light maintenance. As long as you clean the lint filter after every load, you are already committed to taking care of your machine. Once in a while take a peek into that slot where the lint trap goes into (only if its on the front of unit not the top) sometimes you get a buildup of lint and you want to use your vacuum along with a long brush. Look out for objects such as socks. Sometimes those end up in there and get caught by the blower fan which leads to other issues. Do not use a plastic-like flex hose exhaust tube on back of dryer, that will eventually catch fire. If you have one of those, you should replace it with a foil flex hose exhaust tube. Those are way firmer and won't catch fire. You also want to make sure that you check that tube about every three months to make sure that there is no excessive build up of dust there. The ducting in your house needs to get cleaned out by a professional once a year approximately depending on how much laundry you dry. If this exhaust gets clogged with lint, then when your dryer is trying to blow the hot air + moisture out and it can't, it becomes forced and will damage your dryer which will cause the thermostat to open and will not allow your dryer to heat up any longer until serviced by a professional.
Dryer not starting?
Check for power. If you are not knowledgeable of how to, get someone that knows how to do this part. If you have an electric only model then you are looking to have 240 VAC. If you have the gas model then you are only looking for 120 VAC. Usually not starting is a sign of a bad door switch, do a visual inspection. Other reasons may include a broken drive belt, bad motor, bad thermal fuse, or bad control/user interface.
Starts but stops?
Bad motor relay, loose door which affects the door switch status, control/user interface, bad motor, or clogged exhaust.
No heat?
Bad heating element, bad safety thermostat or fuse, bad operating thermostat, bad control, bad gas valve coils.
Won't turn off?
Bad timer or control. Bad door switch.
Clothes are not drying or taking too long?
Clogged exhaust, bad moisture sensor, bad timer/control.
Unusual squeaky sounds or grinding?
Bad idler pulley, broken drive motor-fan assembly, bad drum rollers, bad drum glide bearing.