Well established casino will offer you a wide selection of games to play which you can also find at traditional land-based casinos. At least you will find Blackjack, Craps, Poker, Roulette, Video Poker and Slots. Many casinos offer additional table games like Caribbean Stud, red Dog and even Casino War.
Nowadays many online casinos have multi-player versions of the more popular games: Roulette, Blackjack, Texas Hold'Em, 7-Card Stud, and so on. Multi-player means that more than one player can participate at a time playing the same game.
As for Slots there are hundreds of different slot machines online, you will not find such a selection in Las Vegas. Single line, three line, 3 or 5 reel, progressives, bonus games and many other types. Every Online Casino tries to have it's own version to attract players.
All these games are easy to play, but even if you are new to online gambling you have a lot of information available on the Internet.
Remember, that one of the important pros of online gambling is that you can always find the rules that offer you a better chance to win. For example, if you play European Roulette you have better odds as compared to American Roulette.
As for blackjack, the rules vary from casino to casino. Everything from 1 to 8 decks of cards can be used, at some casinos you can double on any two cards, at others you can't and so on.
You will hardly find a well established online casino that does not allow you to play for free. It is always a good idea to practice your chosen game in free play mode as it gives you the chance to check out their software before you spend any money.