Google Arena GUI & download it. Then google "chesslogik" and download fire UCI engine. There you go.
Best Free Chess Software

So, just to make sure I get this straight: I download both a GUI and a computer engine, which must be compatibile with each other, correct? Also, what are the differences between GUI's? Do some just have better features, or do they all do the same things but some just are cleaner and easier to use than others? Does anyone else want to weigh in on two programs that would work well with each other? Do some engines work better with certain GUI's?
Also, is Rybka 2.2n2 any good? I believe it's also free. I've also seen something called Babaschess - is this program just for FICS, or does it work well for other functions?
One more thing: I have a laptop - how will that effect my performance/options?
Also, thanks for the suggestions philidor_position.
Okay, one more thing: is there anything else I should get in addition to the chess engine and GUI?

GUI is the interface, the car, if you will, that the engine will run on and communicate with the user. The strength of analysis is completely determined by the engine and not the GUI, but GUIs have different options of analysis and different ways of presenting analysis results etc, so yes they do make a difference.
Alternative free GUIs are SCID, ChessDB and not exactly free but also chessbase light. The commercial GUIs like Fritz, Chessbase, Aquarium, Chess Assistant etc have more detailed and various options and some (definitely NOT aquarium) are more user-friendly. You can google about each of them if you want to learn about their features.
Rybka 2.2n is another free engine, it's an older version of Rybka, but firebird and stockfish are much stronger than that.
Having a laptop vs desktop shouldn't make a difference in analysis strength, it's completely up to the CPU power of your computer. However overheat may become a problem in some laptops if you analyze for long periods of time.
Babaschess is an interface for the chess server FICS, I suppose you can analyze games in there with an engine too, but I don't know how and I don't think it would be easier to use than Arena or other GUIs.
Alright, thanks again, that clears everything up. I'll just research the various mentioned programs on my own, and if anyone else has anything to chime in feel free to!

Google Arena GUI & download it. Then google "chesslogik" and download fire UCI engine. There you go.
Thanks for mentioning the GUI and engine. The tools seem really interesting. Can you recommend some other free or commercial engines?
Just downloaded Arena - during the setup process it had a long list of engines that I could include in the download, and the largest (=best ?) was Rybka 2.2, so I just kept that in the download to simplify things. I may go download another engine later (how would I get it integrated into Arena?), but right now I think I'm okay. After glancing at it, it will take me awhile to learn, and I'll post back here again with my thoughts on the software, because as of now I have yet to use it to analyze my games.
Quick Edit: Can't really figure out how to phrase this properly, but is there a way I can get it to suggest me moves, or something like that? For the opening, mainly. I'm thinking something along the lines of the game explorer on here. For example, I play 1. d4, then I move 1... Nf6, and I want to know the most-played move or the best move in this situation (not the best example, I know). The setup also included a download of a database of quite a few games. Any other ways I can utilize the database?

Quick Edit: Can't really figure out how to phrase this properly, but is there a way I can get it to suggest me moves, or something like that? For the opening, mainly. I'm thinking something along the lines of the game explorer on here. For example, I play 1. d4, then I move 1... Nf6, and I want to know the most-played move or the best move in this situation (not the best example, I know). The setup also included a download of a database of quite a few games. Any other ways I can utilize the database?
You have to find a database of games somewhere, I'm not sure how to set it up in Arena, as I use SCID, but I'm sure you'll figure something out.
Download enormous.zip here:
Index of ftp://ftp.cis.uab.edu/pub/hyatt/pgn/
it's about 275MB, and kicks you off with about 1,500,00 games.(free download). Rename it with a pgn extension when you're done unzipping.
Another good free engine is Robbolito, which works well with SCID.
[edit] You should load this database into Scid (or Arena), and open a tree window. This window will show you the frequency and success rates of moves.
Yeah, I believe mine "came" with a database.
I tried to analyze a recent game of mine, but I just don't know. This thing is difficult to use/understand. Is SCID easy to use? Maybe I need to give another GUI a try, or attempt to get Arena to work better.

None of them are "easy", you have to play around a bit, and learn as you go on. I did download Arena, and had a quick look, SCID seemed better to me. But that's personal choice, I think. If you have questions about SCID, post here, or PM me and I'll try to help.
Alright. I'm thinking I'll probably download SCID and mess around with both of them when I feel up to it. Thanks for the help everyone!
I use SCID as my GUI and Stockfish as my engine (mostly because I use Ubuntu and they were easy to grab via the repositor).

play around with arena--it really is pretty decent once you get past all the confusing things lol!
i have found that chessbase light is a NICE GUI for use with engines. while it does help if you are familiar with fritz or chessbase products, it's free, and very reliable. you can find it doing a search on www.chessbase.com. :)
i personally sprung for fritz, and use shredder 12 on my linux machine. both are amazing, and so easy to use it's ridiculous. :)
Hello,
I'm pretty new to this website and recently started getting much more serious into chess. As a result, I've been thinking of downloading a chess engine that I would be able to use to anlyze my games (well, the few good ones that I have). What do you all suggest is a fast, easy-to-use, free chess program that I can download on the internet to improve my play?