Nothing- from out of your pocket, anyway.
A contingency fee is used by lawyers in most personal injury cases. The fee is a portion of your monetary recovery paid by the insurance company in settlement, usually 1/3. You'll likely be responsible for paying the costs incurred by the lawyer to help your claim, but these expenses are usually paid from the settlement, along with the fee. The fee is computed before costs are deducted.
For consumers the beauty of a contingency fee is, we don't take your case unless we're pretty sure we can help you. The benefit to society is, it discourages lawyers from filing frivolous lawsuits- if we don't think you have a meritorious case that should be paid, we can't get paid, so we decline the case.
There are other benefits of a contingency fee. It helps give more people access to justice, since hurt people typically don’t have the money to take on giant corporations or their insurance companies. And it protects you from the lawyer spending way more time on your case than you both expect– it doesn’t change the fee like it would if you paid him by the hour. So you don’t have to be scared to death checking your mailbox every first of the month for an enormous bill.