Bluffing on the river is a really import tool in your poker strategy. It can be very expensive or very lucrative depending on your skill.
To find the right spots and the right opponents is an art that usually takes many years of practice. A few guidelines on bluffing in general might be a starting point.
Since when you are on the river there are no more cards to come and you usually have a good idea if you have a hand that it is worse than your opponents. So it is easier to see whether betting is for value or a bluff.
So let’s imagine a scenario where you are almost certain your hand is weaker than your opponents. The only way to win the pot is by bluffing.
Now the essential skill is to determine if you should bluff – and if you do how much you should bet.
The more you bet the more likely opponent is to fold (usually). So before you decide to bluff on the river you need to estimate your chance at success. But the more you bet, the higher the risk.
If you bet the pot you need at least 50 % of success for a bluff to be profitable (1:1 odds). If you bet half the pot you need at least 33 % chance of success to be profitable (2:1 odds). If you overbet the pot you need to be successful a majority of the time.
Think about the likely hand range of your opponent. Think about which hands in this range he will likely fold if you bet considering what you are representing and how well that matches your likely hand ranges and the story. And try to estimate how large part of his hand range that he is likely to fold.
The easiest way to get the thought process started is by considering a pot sized bet. Will it succeed at least half the time? If you don’t think it will you should probably not make the bluff unless the circumstances are special (for example an opponent who always fold to an all-in if he doesn’t have the nuts). If you think it will you can adjust the actual bet to a suitable size depending on the situation and the opponent.