Knowing when to continue bet and when not to is a very important skill in any poker game, none more so than a 6 handed cash game. This tip is aimed at the 6 handed game but will be applicable to other forms of poker as well.
Firstly, if you are out of position, you should be much more inclined to bet than when you are in position. This is because when you check to someone on the flop you are making it very easy for them to steal the pot, whether they have a hand or not. The second factor to take into consideration is the number of opponents you have. You should only ever continue bet (with no hand) when you have two opponents or less. Any more and unless you are up against very tight opponents you are a big favorite to get called.
As well as when up against multiple opponents, another time to consider checking is heads up in position when you have raised with a hand like AK/AQ and missed the flop completely, if you are against a loose passive player. This player is likely to have missed the flop as well, and you will often get to a showdown for free. This player is likely to call any bet with any pair anyway.
You should always bet if you have missed completely and have no way to win a showdown. For example 67s on a 2 J A board.
This is a mistake that a lot of players make. They raise with a hand like AK or AQ, an opponent calls out of position. They miss the flop and both players check. Then the turn doesn't change the board, their opponent checks and they bet. This line to even the worst of players makes your holding very clear. You have missed over-cards! The player who checks out of position on the turn will know exactly what you hold and will only every fold if he can’t beat you at a showdown anyway. From time to time he will raise with a hand that you beat!
You are far better of checking behind on the turn, this gives you a free card which will sometimes win the hand for you. Also you can call a bet on the river from time to time with just ace high. This is a much better way to have money going into the pot then betting the turn, as you will be often calling a bluff. When you bet the turn you are stopping your opponent from bluffing you (except for a bluff raise on the turn, or a call then bluff on the river, neither of which you can call!) and bloating the pot.