The Chaos Space Marines consist of the legions that followed the traitor Horus in his crusade against the Imperium and the Emperor of Mankind. After Horus fell in battle the remaining forces were routed and driven into the Eye of Terror, where they currently reside and launch Black Crusades against mankind. Currently, there are Chaos Cults all over the place, and any race can come under the influence of the Chaos Gods. However it is the Chaos Space Marines that form the vast majority of the threat.
The Chaos Space Marines play a lot like the Imperial Space Marines, i.e. they are insanely tough, have very powerful wargear, great weapons, and each single piece is a threat. However, unlike the Space Marines, the Chaos Space Marines have the servants of their dark gods fighting along with them. It is through these demons and the Marks of Chaos that make this an interesting army to field.
The typical Chaos Marine is very similar to his Imperial counterpart, very strong, good armor, bolt gun. As far as that goes there is very little difference between the two armies. Unlike the Space Marines, the chapter of an army does not matter, it is which one of the gods they worship that dictates what powers and curses an army will have. There is plenty written about the Chaos Gods, so I don't feel the need to discuss them except to say that the God that gives your army its blessing does make a difference in gameplay. I have played with an army of Khorne and Tzeentch, but not Nurgle or Slaanesh, so I don't know how they work as well.
Note: my army is enormous, and in a tournament I only use the Khornate troops, for those of you who don't like homebrew rules and tremble at the thought of combined forces of Chaos
A Chaos Space Marine army is almost always a work in progress. I've been building mine for a few years now, and I'm still adding to it. To start, I would recommend the same thing I would to a Space Marine player, start with a good solid core of marines and play a few games. Take notes, see how you play, become familiar with all the units, and fill in the gaps of your army in the order of the most critical problem. What you should not do, is base your decision on the Greater Demons, they are all very cool and incredibly powerful, it is the other things available through the blessings that should tell you what to do.
For those of you who don't want my advice, don't read on; for those who might, I have been playing Chaos for quite a while now and would like to think I know what I'm talking about.
First of all, how do you choose which god to devote yourself to? If you play with friends and agree to use some of your own rules - nothing obscene- I would recommend a combination force, as I said Khorne and Tzeentch cna make for a really tough army. If you're playing in tournaments, I recommend choosing a god and making a really good army. As far as individual gods, I would have to say Khorne and Tzeentch are really good, if you can combine them you'll be nearly unstoppable.
Slaanesh is the one I'm most hesitent to recommend, because the units you can use aren't as useful as some of the other gods'. While I agree Noise Marines are damn annoying to your opponent, they function much the same as Devastator Marines and aren't good if you're forced into a lot of melee combat. On the other hand, they look really cool as do most of the other Slannesh units and on top of that they're pretty tough. I won't knock Slaanesh armies because I've seen them used quite well and they are capable of a lot, I just like some of the other gods better.
Nurgle is pretty much along the same lines. Plaguemarines are some of the most annyoing units to fight against, they're some of the toughest units I've gone up against. The Great Unclean One has a terrible habit of not being dead. You can focus a lot of firepower on that beast and it'll shrug it off and rip your forces a new one. If, for whatever reason, your units take a lot of pounding in an average game, definitely think about a Nurgle army, the bastards just don't die.
Tzeentch, hmm Tzeentch is one mean bastard. Chaos Sorcerers, strike fear into the heart of any servants of the false Emperor. Then there's Ahirman, who is a mandatory character if you're going to play a Tzeentch army. Definitely don't ignore the Thousand Suns marines, they comprise of the sorcerers as well as a really nice group of soldiers. A nice group of these and you'll have the Imperial war machine limping away with its tail between its legs. When you bring along the horrors and Flamers and top it all off with the Lord of Change itself, even Marneus Calgar and the Ultramarines are going to have a hell of a time not getting butchered.
Now we're at my favorite of the gods, Khorne. With Khorne, there is a very simple strategy that involves sending in a whole bunch of troops to rip apart your foes and bathe in their blood. The real beauty of a Mark of Khorne isn't anything terribly complex, merely that Khorne Berzerkers can be taken as a troop choice, instead of elite. What does that mean? It means you can take a whole lot of them, and they are perhaps the best close combat troops in the game, as long as they have enemies to tear through. Those along with the Juggernaught, flesh hounds, Bloodletters, and the monstrous Bloosthurster make for an army that can quickly sweep anyone else off the table. Also, don't forget Kharn the Betrayer, while he may end up attacking your own troops, I have been able to use him to take out every Imperial hero, which makes him well worth the cost.
Your final option is Chaos Undivided, which means you'll have access to most anything, but no blessings or benefits. Doing this makes for a more well-rounded force but with fewer really nasty units and plays almost exactly like the Space Marines only without the And they shall know no fear rule. It is definitely an option, and there is nothing wrong with it, but if you want to play like this I would really recommend playing the normal Space Marines, it'll end up being better in the long run.