Personal injury attorneys accept cases on a "no recovery, no fee" basis. In other words, the client does not pay his lawyer anything "up front." If and when money is recovered, the attorney receives a portion of it as his fee. This is called a "contingency fee," because receiving a fee is contingent (i.e., dependent) upon the success of the claim.
The amount of the fee depends upon the prevailing practice in your geographic area. The usual fee for adults and children is 33 1/3% of the total amount recovered, rising to 40% if the case goes into litigation. About 98% of cases settle without the necessity of a trial. However, when the victim is a minor when the case settles (not when the incident occurred), some courts reduce the fee to 25%.
In addition to providing services without an "up front" payment, personal injury lawyers use their own money to pay for the costs of making the claim, at least until there is a reasonable settlement offer. The client is not asked to contribute toward costs. At the conclusion of the case, the lawyer is reimbursed for whatever he expended on the direct costs of the case. Like the attorney's fee, reimbursement is contingent upon the success of the claim. However, the client might be required to pay costs if he refuses to accept a reasonable settlement offer which is recommended by his lawyer.
The costs of making a claim usually are relatively small, compared to the amount of money that will be obtained. In an average claim, they might come to between $1000 and $2000. However, cases that are being prepared for trial become very expensive -- tens of thousands of dollars. Fortunately only 2% of claims actually go to trial, so there is no significant risk of the costs "eating up" the recovery.
It should be noted that the contingency fee system is uniquely American and that it has been under attack in recent years. Because it enables ordinary citizens to obtain legal help, the corporate world -- insurance companies and other industries -- has been trying to pass laws to abolish or cripple it. These laws take several different forms, such as an arbitrary limit on the amount that a victim's attorney can charge. Note that only the victim's attorney would be subject to any limitation, while the insurance industry's lawyers would continue to not only charge their usual hourly rates but also rely upon the vast monetary coffers of their wealthy clients. The tort system exists for the benefit of ordinary people as opposed to the interests of the business world, and therefore the system and its key players (the victims and their attorneys) constantly suffer attacks and constantly must fight for their rights.