The modal auxiliary verbs would, could and might can be used to make questions, suggestions and requests less direct and therefore more polite.
I thought I would take a day off work.
Hi! I thought I would come over and introduce myself.
I thought I could borrow your car.
I thought you would lend me a pound.
Could you help me wash the carpets?
I was wondering if you might be interested in a game of chess.
I was wondering if you could lend me a pound.
Could you give me a hand?
We could ask Peter to help us.
It would be better if you turned that music down.
Would is commonly used before verbs of saying and thinking. The purpose of using would in this case is to make a statement sound less definite.
That is what I would call annoying.
I would think we might stop for lunch soon.
I thought you would like this.
The modal auxiliary verbs would and should are often used with other verbs that refer to unreal or uncertain situations. This usually happens in sentences with if.
It would have been nice if you had thanked him.
I would tell you if I knew.