Let's say it is the final round of betting. The pot is $10, your equity vs your opponents range is 20% (a probability of 0.2 that we win) and you don't know what to do. You are first to act vs one opponent.

1) You check and your opponent checks:

Your Expectation = 0.2*($10) = $2.00

2) You bet $2 and your opponent calls:

Your Expectation = 0.2*($10 + $2 + $2) - $2 = $0.80

3) You check, your opponent bets $2 and you call:

Your Expectation = same as in 2)

4) You bet $2, your opponent raises it to $4 (he calls your $2 and adds $2 more), you call:

In this case, the raised pot totals $16 ($10 + $2 you add + $4 opponent puts in) and it costs you $2 to call -- that's 12.5% pot equity and you have 20% equity to win! But...

Your Expectation = 0.2*($10 + $2 + $2 + $2 + $2) - ($2 + $2) = -$0.40

If you want some sort of equation for Expectation, it's basically:

Expctation = (probability we win)*(size of new pot) - (what it costs you)

Things get more complicated when we're looking at catching draws and things on later streets, but i'll post on that eventually.

N.B. This is for those times are equity is less than 50%, since we want to bet/call (or bet/raise) when we have better than 50% equity.