"I will appreciate your help"

Solution 1:

Normally one would say

I would appreciate your help.

That is a softer, more polite way of asking. Use of the subjunctive mood indicates that nothing is assumed. It is a shorter way of saying "Should you be so kind as to give it to me, I would appreciate your help." [Edit: @As Eldros notes, to show appreciation for something is to be thankful for it. The example above could be paraphrased as "I would be in your debt if you would be willing to help me out."]

Using will instead of would seasons the sentence with a stronger flavor of expectation:

I will appreciate your help.

This is what you would say if you were fully expecting — perhaps even demanding — a person's help. It is something someone who has power over you might say, and is pretty strong. If the person is actually asking for a favor, this phrasing is very likely to offend the respondent.