Here's how it generally works: Going All In: If a player doesn't have enough chips to match a bet, they declare they are going "all in." They then push their remaining chips into the pot. Creating a Side Pot: A separate pot, known as a "side pot," is created for any additional bets.
If a player cannot bet the full amount it takes to call (or make the blind or straddle bet), they can bet all their remaining cash. The player is then tapped out. The player keeps playing but makes no more bets (and, in particular, cannot raise).