A ring game is just a game that you play. No start or stop, unlike a tournament. Also you bet cash (or chips with cash equivelant) rather than betting tournament chips.

In a $.50 / $1 this is probably limit. You post $.25 and $.50 as the Small blind and big blind. Pre-flop you can only call, bet $.50 or raise $.50. After the turn you can call, bet $1 or raise $1. There is a limit to every bet. You can buy in with anything from $15 all the way to $150. You're choice.