In case you are the last to play on the river, the situation, of course is much, much better. Your problems now are totally different. After your opponent’s check you evaluate your hand in order to decide is it suitable for increasing the pot size or to bluff. In case it is not, you should check. In case you believe that your hand is very strong comparing to the hand of your opponent, you should place a bet i.e. you should increase the pot size in the most classical waу of doing that.
If your opponent places a bet, try to evaluate again his hand but do not forget that there is a possibility of bluffing as well. Based on your analysis you should make your decision by answering the question: does your hand have enough chances for a call? It is important to know that even for the tightest players the probability of bluffing on the river is not more than 10 %!