This topic interests me and I would like to just add another related question that hopefully any answering the OP's questions or maybe the OP could answer mine too.

Could anyone give a really brief idea of what gels are used for what situations? If this is an insanely broad question to ask, just say so and I will try and do my own research.

That's standard. I've been using clothespin on the barn-doors as
long as I can remember. And every set I've ever been on uses this
method. It seems efficient and very fast to me. Gels are typically an
"expendable" - meaning they are not an item used for many years.
They get crinkled and burned and melted dirty and faded. When they
become unusable (for any reason) you cut another piece.

Gels are used to manipulate the color of the light, the intensity of
the light and the color temperature of the light. There are gels that
diffuse the light and soften the light and there are gels that warm the
color temperature and those that cool it. You use gels to change the
color temperature of sunlight when shooting indoors, you use gels to
change the color temperature of some neon lights.

A great example of using gels to color lights for aesthetic purposes (and a little extreme too) is Chungking Express by Wong Kar Wai. Let me see if I can find a picture to link that describes what I mean...

Here we go,

In this scene the background is a dark yellow and depending on the camera angle can be a bright yellow. The characters are tinted orange-yellow and orange-yellow. Don't ask me why, I'm not good at subtext.

Also here:

In this image, the scene is shot in an incredibly small apartment. The director uses the color, among other reasons, to clearly separate the subject from the background and create depth. You see the background has a green light on it and the subject of attention has a pinkish light thrown on him. Later in the same scene... or maybe it's earlier, I don't remember, the subject is standing and moves backwards about a 2 feet to feed his dog. Both the man and the dog are colored pinkish, while the background is still that jade green.

Lighting is an artform all it's own. It is a many nuanced thing that takes years of practice to do well. I am still very far from being great at it myself.

As it was mentioned above, don't expect your gels to be around very long. They are expendables. The good news is that they're comparatively cheap (when one considers the cost of everything film related).

I find that I don't really use very many colors in my lighting. I always have some Full CTO (color temp. orange) on hand to gel windows to match the tungsten lights I'm using (can't afford HMI :/) I'll also have some 1/2 CTB (color temp. blue) for correcting tungsten to daylight temp. If 1/2 isn't enough, I just double up. I try to avoid the CTB situation as it cuts a lot of light and renders your source pretty much useless unless you're shooting with a hefty light.

Aside from those colors, I might have a few +green for combining fluorescent lights with tungsten, a few yellows and a few ambers in case I need to warm up a light a bit and then a series of diffusion options. Really, the diffusion is what I think is most important. Unless you're shooting a music video, or a highly-stylized piece, most of your color control can be done in post with color correction. I find it most wise to shoot as "flat" as possible and then manipulate in post.

you should try reading the book Painting With Light its pretty neat. It was written by a DP who shot many of the most famous American Film Noir and is arguably responsible for that style.

That book isn't really going to teach you how to light for video but it will give you some cool ideals and more understanding on the history of filmmaking.

Gels could be used to warm up a scene, lets say you want to shoot 2 characters having breakfast you could light the scene using orange, red and yellow creating a warming color.

thats just one idea.

Fortunately, somewhere between chance and mystery lies imagination, the only thing that protects our freedom, despite the fact that people keep trying to reduce it or kill it off altogether.
- Luis Bunuel

I hate to say it, but aside from reading some basic "how to" books on lighting, your best bet is to simply set the camera up, and start playing with several lights until you get the "look" you want. This may seem like an odd choice, but I've been very impressed with the latter seasons of Stargate: SG-1, and their use of dramatic lighting. But, I would stress, just watch shows and movies that you feel are impressive visually, and watch them again and again... and TAKE NOTES.