A. To pour oil on troubled waters
"To pour oil on troubled waters" means trying to calm things down. Oil is lighter than water. If a ship is in trouble at sea, another ship may come to help it. The second ship can send small boats to rescue people. However, it may first pour oil on the sea to make the sea less rough.
B. A bird in hand is worth two in the bush
If I'm a hunter, trying to catch birds, it's better to catch one bird than to see two birds in a bush but not be able to catch them. Thus this means that what you have already got is better than the chance of being able to get something bigger in the future.
C. He who pays the pipe calls the tune
A pipe is a musician. The man who employs or pays a musician can say what tunes the man will play. Thus this means that if a man provides the money for a plan, he can say how it will be carried out.
D. Once bitten, twice shy
If a dog bites me, I shall be twice as careful in future when I see it. This proverb is applied to many things and not only to dogs. If you have been cheated at a shop, you will not go to the same shop again.
E. You can't get blood out of a stone
"You can't get blood out of a stone" means that you can't get something from a person who has not got any of the things you want. For example, you can't expect a million dollars from a poor man.
F. Don't be a dog in a manger
This means "don't be selfish". In a stable, the manger is the place where the horse's food is put. Sometimes a dog will sleep in the manger and bark when a horse comes to get its food. The dog doesn't want to eat the hay in the manger and bark when a horse eat it.