There are many different types of pedals, flats, rat-traps, clip'n'straps, clipless, Shimano, SPD, Look compatible, Time Compatible and many others. But, they all have two things in common, they always come in pairs and each pedal only fits into one side of your crank arms.
Pedal threads are left and right-handed, so one pedal will only screw into the left crank arm and the other pedal will only screw into the right side crank arm. If you don't know which is which though, there's little on the pedal to help you out. So, let us explain and clear up the mystery for you.
Start by identifying the left and right pedal. The left-hand pedal fits into the left-hand side of your crank. This pedal screws in anti-clockwise. When you place this pedal on a flat surface in front of you, with the pedal axle pointing away from your body you will notice that the threads cut into the axle slope downwards from the left. Apply a thin layer of grease to the pedal threads and use the washers to fit between the pedal and crank arm. Ensure when threading into the crank that pedal threads are aligned properly with the crank arm threads, and not at an angle.
In contrast, the right-hand pedal fits into the right-hand side of your crank. This pedal screws in clockwise. When you place this pedal on a flat surface in front of you, with the pedal axle pointing away from your body you will notice that the threads cut into the axle slope downwards from the right. That's the magic. Down from the left = LEFT pedal, down from the right = RIGHT pedal.
When you fit a pair of pedals, greasing the pedal axles before threading them into the crank arms will make them easier to fit, and a lot easier to remove when you do eventually decide to replace them. Start threading your pedals by hand and only switch to using a spanner or Allen key once you are sure they are threaded correctly. If they feel too tight to screw in with your fingers, reverse them out, check you have the correct pedal, and start again.
When fitting your pedals, make sure you do them up to the correct torque- this will be marked on the cranks. If you don't tighten your pedals thoroughly there is a good chance that they will unwind from the crank arm during your first ride- and if that happens there's a good chance that you'll strip the threads as your weight bears down on the pedal and pulls it out of the crank arm, damaging the last few threads and writing-off your crank in the process!
And that's all there is to fitting pedals. It's easy.