Today, thanks to televised Poker broadcasting, running the gamut from the World Poker Tour to Stars You Never Really Liked Play Poker!, No-Limit is probably the best-known version of the game.
No-Limit Hold'em is a vicious and diabolical game, where the rules are only slightly more complicated than "you can bet any amount at any time."
The most common way to see a ring game No-Limit table described is something like "$1/$2." When you do, these are the amounts of the blinds and the lower limits of the betting. The upper limit that can be bet on any given hand is however much any player has sitting on a table.
Buy-in is typically limited to a minimum of ten times the lower dollar figure and 100 times the upper dollar figure, so for a $1/$2 No-Limit game, your buy-in could be anything between $10 and $200. (The other way you'll sometimes see No-Limit described is by the maximum buy-in, say "$200." If you see a single number describing a No-Limit game, this is the maximum buy-in for that game — ask the dealer what the blinds are.)As a general rule, you want to have something very close to the upper limit of the buy-in when you sit down at a table so you're not immediately intimidated (or just flat cleaned out) in a hand by someone with a considerably larger stack.
When you sit at a No-Limit table, you're not allowed to remove chips from the table (that is to, say, pocket some of your winnings) until you leave the game altogether. When you do leave a game, you're typically not allowed to reenter for a specified time limit (usually 30 minutes or more).
In case you haven't figured it out by now, No-Limit is an extremely dangerous form of the game. Just like doing trapeze without a net, the lack of limits on the betting doesn't make the tricks any more difficult — it just makes the penalties more severe. Starting out your Hold'em career with something like a No-Limit ring game is a very good way to watch your wallet walk south.
If you're interested in learning No-Limit, you should play Limit first until you're comfortable, and then move along to small buy-in tournaments.