In all cases, you would want to consider your own hand - what common hands
you would beat and what hands would beat you.
Hand - betting on the strength of your own hand - getting a pair of aces at
the beginning of a game are a great foundation to build upon, but an ace and
king of the same suit have a greater potential for strength. These would
both be hands you would want to bet heavily on.
Opponents - seeing an opponent checking (ie not optioning to bet) means
either that they are second guessing their own strength and do not have a
good hand or that they are trying to lure you into betting more while they
secretly hold a strong hand. In either case, if you are already sitting on
a good hand, bet, otherwise, checking yourself is a free shot at the next
round of cards and betting.
Value betting/return odds - betting 500 chips with a pot sitting at 20,000
is a very good risk when considering the potential return. Know how many
cards are out there and of what suits, and know how many of those cards will
help your hand and how many won't. Use those odds to help determine how
much to bet by figuring that out before making your next move. For example,
if you are going for a flush draw, you know that there are three suits that
won't help and only one that will - those are 4 to 1 odds that you will get
the one card that you need to complete the flush. If the amount in the pot
for a hand is four times more than you'd need to bet to call, than your risk
is balanced by the likelihood of getting one of those cards to win the hand.
Blinds - forced bets are an easy way to get your way into a game - you are
required in some games to bet certain amounts, so you may as well ride
further to see how far that forced bet takes you.