Hourly Fee Arrangement
In this arrangement you are charged a preset and fixed hourly fee. You are charged for each hour the lawyer spends on your case plus any outside costs such as filing fees and stenographer fees.
Contingency Fee Arrangement
In this arrangement there is no charge for for the lawyers services unless and until you win your case. At that time the lawyer receives a percentage of your settlement, which is determined up front, and you will also pay for any court costs and other out-of-pocket expenses that are involved.
There is a fee arrangement common in employment discrimination where there is a combination of a reduced hourly rate and reduced contingency fee. For example the lawyer may charge half his hourly fee plus a 25% contingency fee. This is something you and your lawyer agree upon before the case begins.
There is often a difference between the fees you agree upon and what the court awards. This is something that should be discussed with your attorney.