Learn English – difference between prepare and preparing

The first sentence is correct:

It will help me to prepare for the exam.

The verb help takes either a to-infinitive (to prepare) or a bare infinitive (prepare):

It will help me prepare for the exam.

As Peter said, preparing is a gerund: this word works like a noun. The verb help doesn't take nouns directly, so we need to use some preposition:

Please help me with my homework.
This will help me with my homework.
This will help me in making my homework.
This will help me in preparing for the exam.

There are verbs that take nouns and gerunds directly:

I will try preparing for the exam.
I will try this apple pie.

See? The difference between "(to) prepare" and "preparing" is that the first is a verb and the second is an ing form that works like a gerund (almost like a noun) or a present participle. The verb help does not take the ing forms directly (without some preposition like in, with, etc.) That's why your second sentence looks strange, although the meaning of it is easy to understand.