Generally, lawyers who take on auto accident, slip and fall, dog bite, and other personal injury cases charge a fee of 1/3 of the recovery. Very seldom does a lawyer who represents personal injury victims charge by the hour.
What the 1/3 percentage fee means is that if the lawyer obtains a settlement, or verdict for the client, the lawyer will take 1/3 of the recovery, plus the expenses the lawyer advanced. Some lawyers charge a lower percentage, some charge a higher percentage than 1/3. Some lawyers will charge a fixed percent, but if the case is put into litigation, the percentage fee may increase. It all depends on the lawyer and how he or she structures their contingent fee schedules.
Finally, some lawyers are willing to negotiate the percentage of the fee with prospective clients.