Assume, for the moment, that you are one of those rare drivers who actually uses their turn signals (I'll have more to say about that later). There's not much point using them if they aren't working, right? But how will you ever know if your lights are malfunctioning? You can't see them from inside the car. Or can you?
In fact, most drivers have plenty of opportunities to check their lights, if they could be bothered to notice. Next time you park, pull up close to whatever is in front of you and check your headlights. Even if it's daylight, you should be able to see clearly if they're both working. Then do the same thing for your turn signals.
Checking your rear lights is a bit trickier, but still doable. Next time you're stuck in bumper-to-bumper traffic, take the car out of gear and tap the brake pedal a few times. You should be able to see them in the rear view mirror, lighting up (or reflecting off) the vehicle behind you. Your results will vary, depending on the positioning of your lights and the type and colour of the vehicle behind you. Do the same thing for the rear signal lights, but be careful: you don't want to give the impression that you want to change lanes.
It's best to do these checks in your driveway or in stopped traffic. Don't fiddle with your signal lights in moving traffic. That's dangerous.