Take me to the...
The turn and river are a bit different than the flop. On the flop you are trying to achieve a particular goal without giving away any information about your hand. Once you have hit the turn though you have a lot more information and now the goal is to win the pot. And if you have the best hand you want to make it the largest sized pot possible. The answer as to how much to bet in these situations is 'it depends'.
What it depends on is your opponent and the likely hand they are holding. This is where careful observation of how they play and what their tendencies are will come into play. Are they the type of player to only call with a draw on the flop? Are they the type of player that will call with any piece of the flop, whether it be bottom pair or top pair, weak kicker? Use the information available to you to help you determine how much to bet. If you have a very strong hand that is virtually unbeatable, you want to make a bet that will get called or will induce a raise. If you have absolutely nothing but think you can get your opponent to fold, you need to make the bet that you think will get him to fold.
Protecting your hand
If you have a strong hand but one that is vulnerable, you want to make a bet that will be large enough to get value for your strong hand but at the same time will make it an error for your opponent to call. For example, let's say you have A-K on a KcJc6s2h board. Your opponent just flat called you on the flop and you feel he has either a straight draw or a flush draw or both. Your hand is probably the best but it is vulnerable. You don't want him to fold but at the same time you don't want to make it easy for him to call. A bet of approximately 75% of the pot in this instance would probably accomplish both of your objectives.
The bottom line when it comes to bet sizing is that there is no fixed amount you should bet. You bet the amount needed to get the job done. Being consistent with your bet amounts will help and I recommend doing so pre-flop and on the flop, but in the end it's all about getting your opponent's to make mistakes. And you can do get people to make mistakes with any size of bet as long as you are paying attention to how they play.