If you want to jump right in, you should really honestly try out Game Maker; there are several great tutorials that can get you running with the drag and drop interface, then you can start learning to replace the drag and drop stuff with GML (the built-in programming language that makes it all work).  If programming in GML just doesn't feel right to you, then you may not want to go into Computer Science.

That being said, the absolute best way to see if Computer Science is best for you is to take a programming course or two in high school; it's all really basic stuff, and you'll have to keep in mind that they may not teach you the absolute best practices for certain things, but it will definitely give you a taste of what programming is like.

NINJA EDIT: If you want to actually get into the *design* part of video games, though, Computer Science isn't the best major to go into.  There are a few schools with Game Design majors (I should know; it's what I started college majoring in), and those are the places you want to look at when looking for a college.  In the meantime, grab a copy of Unreal Editor (it comes with most Unreal games; I'd recommend buying the PC version of Gears of War, as the Gears of War editor is a nice version of the Unreal Editor), find some friends, and start making maps.  This is exactly how my roommate (who worked at Midway, worked on the IGF game Devil's Tuning Fork, and is now working at Wideload Games) and I did things (we made a few Game Maker things together and a Gears of War campaign mission and those are what he used to get his job at Midway), and it works out very well.

TL;DR: If you want to go into design, grab Unreal Editor and dick around in the map editor. If you want to go into programming, take a class or look up Game Maker tutorials.

Computer science is fine for your purposes. It gives you the generalized tool-set that will allow you to go through any technical problem you might encounter in a very straightforward manner. Also, with the right portfolio, a CS degree can take you farther with prospective game development companies in terms of skills you offer than would some "specializedd" game design program. It is also more fun to learn the interesting design-y parts of game design on your own anyhow. (all you need for that is passion, confidence, and an ability to identify/admit when you've done something wrong) I personally found it a relief to leave all the boring parts to the structured institutionalized setting, and figure I can get any type job I want, while still having the game development chops to enter that specific business in any manner I desire.

Although you do need to see if that kind of stuff matches your interests first. If you just see programming as only a means to accomplish better game development, you would most likely be much better off going strictly for a degree designed for game developers.

I'd suggest looking up Python and PyGame. The language is one of the most elegant you'll find, and very good to learn with. While the game library it has is free for anyone to code and make games with, and by comparing that method of development to something like GameMaker, it's easy to decide what kind of game design/development aspects you are really looking to accomplish. (I would argue that both can develop 2d games equally quickly, It's all based on how the user applies the tool sets each offers)

I guess I should clarify something: I switched out of the Game Design major into Interactive Media and have never looked back. Most technical majors, at least at my school, are almost entirely what you make out of them.  EDC is right in saying that, with game design, it's mostly going to be stuff you learn on your own.  If you end up liking Computer Science, go for Computer Science, but if you are more into the design aspects... well, Computer Science is probably not going to be your best bet.

I was thinking of getting into computer science in college so I can get a job in game design. Problem is I'm not sure it's something I wanna do. Is there I cheap (or free) way to dip my toes in the process? Something simple, like with internet games, but something that will be similar to an experience in game design. At least to an extent.

this is my thoroughly unqualified opinion but.

you don't need a computer to make games. use pen and paper if you just want to practise making games. i've been helping some friends design a pen and paper roleplaying system and that shit is so relaxing - when you don't have to bother actually programming you can really flex your design muscle and evaluate the results immediately. you do have to keep in mind, though, that people tend to make games more fun by themselves - kids can play the worst mmo in the world all day and have the time of their lives because they get on with the other kids that play it.  if you can get past your amazement at your own brilliance and think critically about the things you design in noncomputer mode, you can develop your thought about game design in the most general and abstract sense.

secondly, do everything fucking else. tend your garden. take baths. read books. rob liquor stores. make faces in the mirror. all the shit you are good at can go into games. there's interesting books about game design specifically but i don't think you have to read them if you don't want to. some of the best shit i have ever thought about games has been thought reading about graphic design or exploring theoretical computer science ideas. these also give you the surrounding media that make up your multimedia video game, assuming you like graphics and music and writing and things. i think game designers should also learn to program well. this is not so that they can code things from scratch in assembly to prove how mighty they are. it is because computation is an extremely powerful metaphor for describing interactions, and should you miss it you may end up thinking that games are generic coathangers for you to put your artworks on, or at least being forced to treat them like that. written literacy is also very important, but i'm probably not the greatest person to talk about this. i still feel in deep water when trying to talk about fancy literary theory concepts or discuss books. it's kind of two sides of the same coin (unsolvability of halting problem / incompleteness / chaitin's number ~= impossibility of perfection / deconstriction / pharmakon) as far as I can tell but I know more about the side that has computers in it.

thirdly, play lots of different games and think about them carefully. this kind of goes without saying and applies to everything else. analysing things helps in making them. you get the same advice from programmers, writers, film makers, academics and whoever else. know your medium. knowing the parts you hate probably helps even more than knowing what you like.

i think that 'game degrees' are mostly given by unqualified dorks to entertain the fantasies of children. there may be exceptions but I have not seen them. i say this not as a Professional Motherfucker With Lucrative Career. I am not one. making up games is my hobby and maybe the big idea that glues the rest of my brain together. i'd like to do it for a job one day but it kind of fights with my desire for everyone else to have the opportunity to make games. i think that game making shouldn't be a special activity for idiots in suits with degrees. i think that making games can change your life for the better, whether or not you get paid. if you just want games as a lucrative moneycareer thing then I have nothing to say to you - we don't think the same thoughts.

woah that's a lot of text i wrote there. calm down biggles it's just a video games.

it was a big ol' post but i agree with it biggles

in addition to that though, there are some design documents online for existing games.  i feel like there was one for grim fandango???? but maybe i just made that up.  anyway, try reading one and playing the game it's for, and see how the design translated into the game.  otherwise just do what biggles said.

I can't remember if the design document is out there, but I know that the pitch for Planescape Torment (which more or less just worked as a distillation of the design document) is out there and can be found pretty easily, but since I'm at work right now I can't be arsed to do it. Maybe I'll edit this post later.

I'm 80% sure that the Grim Fandango design document was released, I think that would be a really good one to look at since point and click games are pretty clear in how their design translates to the finished product usually.

John Carmack once said you don't need a game design document

John Carmack once said you don't need a game design document

He also once said "Story in a game is like story in a porn movie. It's expected to be there, but it's not that important."

If that's so dumb how come he's a billionaire

And if you want a story then go read a book

Design documents are for the sake of formalities and makes it easier with working on a team by standardizing the material while explaining every angle to every people who would do the various aspects of the game.
For those who have truly made a game, though it's starts on the scratch and brainstorm mess of a paper, you would and you will end up organizing it somewhat in some way. The biggies just had their millions of messy papers into a document that though might seem too formal or clean to our taste, does the most efficient job without suffering any creative damage.

I was going to say game design documents are only useful if you're working in a office with other people but it's a spam bot topic

But anyway nobody was really stressing the IMPORTANCE OF A GAME DESIGN DOCUMENT it was just a conversation about game design, and reading a document for an already-existing game is helpful to see how the design process leads to a game.  Doesn't mean you have to make one yourself.

Also spambot topic or no, this is something a bunch of people want to know and this gets asked quite a bit so no harm in answering it.

Only if they log every change they make into the "game design", otherwise you're just looking at a finished product which you can't always figure out how it got to that state

I think you're mixing design and development.

It's ok because designing is a part of the development itself

Here's the Grim Fandango Design doc if anyone wants to save the trouble from searching google:
http://cache.kotaku.com/assets/resources/2008/GrimPuzzleDoc_small.pdf.zip

Just kind of skimmed through it and actualy enjoyed bits of it. It's not very formal, but it's clean and well organized, obviously refined so the process of redesigning it is not shown. Some bit f art and dialogue to describe the flow of the game. Charcters, maps, etc..
Personally, I think the document is meant to be inspirational.