Here is what you need to do if the transmitter (remote, clicker) or the key-less entry doesn't work: First of all check the batteries. Some transmitters have an LED light which will let you know whether or not your battery is fresh. If that's not the issue, then check your wall button inside your garage. Some have a vacation lock on them. If yours does, the light will be blinking. Simply press and hold the "lock" button. This will deactivate the vacation setting. Also, your transmitter (or key-less) may have lost its programming. In this case you'll need the instructions for the brand you're using. If you need a new circuit board then you need a service call and leave it to the professionals.
Another problem you may encounter is that your motor is running but the door is not moving. Most likely your gears on your operator are broken which will also require a service call. If the door does open, but only for 6" and then it stops, check the coil springs above your door. If there is a separation in either one of them, you need a new spring and a call to a garage door company. As a side note, if your door has two springs, they are probably the same age and the other will break soon, so it's better if you replace both of them as this will save you inconvenience and is less expensive.
If the door opened but it won't close anymore, try holding in the wall button. This is an override for your photo-eyes. If this works, then your photo-eyes are misaligned, there is an obstruction, or they are broken. Check the LED lights on the photo-eyes to see if they are on steady (color doesn't matter). If one or both are flashing, check for obstructions. If there are no obstructions, move the photo-eyes to realign them. If neither of these solutions work, you need a to call a garage door company.
If the door is crooked you may have a broken or unattached cable. This will also require a service call, but at least you know you'll be fixing your garage door. However, if your doors have many other problems and the professionals you called to take care of it tell you that you need garage door replacement, it's probably best to listen to them and make an investment.