Can I install a gears cassette on a regular bike? I was given a bicycle for my birthday (yai!), it has 24" wheels and it is awesome!

But it is single speed and sometimes it is hard to ride up-hill in my daily commute. 
Could I change the rear gear for a gears cassette? 
If so. Do I need to change the rear wheel as well?

PS. Am I using the correct terms? I'm new using english to talk about bicycles.
Converting your single speed bike to geared one is probably not worth the effort, for several reasons:


Cassettes and hub gears both need different kind of wheel hubs than single speeds. You will need to change the whole wheel.
Single speed bicycles usually have narrower rear fork spacing (distance between rear fork dropouts) than geared ones. Your rear fork might not be wide enough to accommodate any geared hub.
Being single speed, your rear dropout most likely doesn't have hanger for a derailleur. Add in parts, and derailleur than can be mounted on the axle do exists, but it adds extra layer of trouble for the whole enterprise.
The frame of your bike probably doesn't have any cable guides either. You will have to either find add in guides, or use makeshift solutions.


In short, I wouldn't try it. It might not be possible at all, due to rear fork spacing. Even if it is possible, it's going to take money, special tools and quite some time put functional gears on your bike.