Бы (would) может/может быть (may/might)

You can add Бы(bi) to any past tense of a verb. Like:
Я пошла в кино (I went to a movie) - Я бы пошла в кино (I would go to a movie)
Он позвонил (He called) - Он бы позвонил (He would call)
So, how does it feel? There is a subtle difference between Russian and English "woulds":
I would buy a house - The act of buying could be happening present through future.
Я бы купила дом - The act of buying covers past, present or future.
I would have bought a house if I had money - Could have happened in the past.
Я бы купила дом, если бы были деньги - Could happen in the past, present or future.
Another difference: in English you only need one "would" in a sentence, in Russian "бы" needs to go with every verb in a sentence.
Also, in Russian you can put "бы" before or after a verb:
Я с удовольствием пошла бы в ресторан, если были бы деньги.

Using "might" or "may" is a little different. In English we use a verb in the present tense with it: I might call you; I may call you; but in Russian you would use the verb in the future tense: Я может позвоню; я может быть пойду.
It makes more sense, actually, because when you say, you might do something, you mean in the future.

In cases when the noun or pronoun is changed to a form when something is done to it, or, sort of, like saying "me" instead of "I"; for instance: мне, ему, ей, им, тебе, коту, девочке, use the infinitive form of the verb:
How would I do that? - Как бы мне это зделать?
How would I eat? - Как бы мне поесть?
When would she go - Когда бы ей пойти
Where would he hide - Где бы ему спрятаться
This might not make any sense to an English-speaking person, because there simply isn't a way to say it like that in English. You just can't say, "How would me eat," or, "Where would him hide." So you might wonder why one would say it that way at all. The subtle difference between A:"Где бы мне поесть?" and B:"Где бы я поела?" is this: A implies that I would like to eat somewhere soon, B could mean that, but also could mean, where would I have eaten, which isn't as precise.