How does forex trading broker profit?

It depends which type of broker you are talking about.

Some will profit by trading against you since over 90% of people fail,

some profit on the spread and some have a commission for each trade.

To better understand the types of broker you can search for the following:

Market makers / Bucket Shops

STP / Straight Through Processing

ECN / Electronic Communication Network

You can understand the hierarchy better using the related link I have added.