> Why do a continuation bet ?
Continuation bets are a standard practice because, statistically, your opponent would have to defend way too often if they wanted to call all your continuation bets. Let's consider a continuation bet size of 25% of the pot with zero equity (like, 72o on a board AT3 rainbow). Your pot
odds are then 0.25/1.25 = 0.2, so you have to succeed in
bluffing only 20% of the time in order to be profitable. So even if you don't connect, it might be still profitable to continuation bet.
> When is the best time to do a continuation bet ?
That's probably the hardest part to figure out. When deciding whether to c-bet you have to mainly consider three things: how does your range stacks up against your opponent, how strong is your made hand, what position are you in, and whether the flop connects well with your range. Typically a preflop first to raise will have range advantage, especially when called by later positions (like UTG vs BTN or UTG vs BB), which is why the pre-flop aggressor will c-bet more often. That said, when the range difference is not that big (like UTG+1 calling UTG raise), the player in position should c-bet more frequently. Then, you need to consider how strong is your hand. With premium
hands and draws you can pretty much c-bet your entire range. With marginal hands and junk it depends on your range. If your range is stronger, c-bet more often. If your range is weaker, c-bet less frequently.
> What table position should you be in to do a continuation bet.
Your position alone does not matter. What matters is what is your position in relation to your opponent.
> When the flop comes and it's of no interest to you do you still do a continuation bet ???
I covered it in the earlier response, but to summarize: if your hand hasn't connected with the flop at all you should bet if you either have range advantage or position.