"Can/may/will you help me with this?"

As waiwai993 answered, Can/May/Will have different meanings. However asking someone if they can help you usually implies that you would like their help, and it gives the person an opportunity to decline without being rude. Maybe they are able to help in theory, but can't right now because they are too busy. In that case they can say that they can't help. If they simply don't want to help they can just decline without a reason. So I would always use "Can you help me with this" or "Could you help me with this" unless I needed a more specific case (such as I KNOW that they CAN, but I am forcing to answer whether they WILL or not, or I know that they are ABLE, but maybe their mother won't let them*).

* Note: I think it's very unusual to use "May you help me" and would probably never say that under any circumstances, unless I was trying to be ironic.

I would actually offer a couple additional options:

Under condition 1 (that you know that the person is able to help, but you're unsure if they will):

Would you help me with this?

Under condition 2 (you're unsure if that person is able to help):

Could you help me with this?

These are similar in meaning to will and can respectively, but are a more polite way of asking. I would especially recommend these if you're in more formal setting, talking to strangers, etc.

Can you help me with this?

Technically, this asks if it is physically possible for the other person to help. However, it is commonly used to mean "Will you help me with this?"

May you help me with this?

This is equivalent to "Are you permitted to help me with this?"

Will you help me with this?

This is the one you probably want—it basically asks whether or not the other person is going to help.