Talk to the lawyer. The easiest way to learn how many cases a lawyer wins or loses is to talk to them. Some attorneys keep this kind of information and can tell you their history, white others may not. All lawyers will be able to tell you, in general, what their history is.
Search PACER. If the attorney has practiced in the federal court system, search the PACER electronic records systems. You'll have to sign up for the service, but you can search through any cases filed in U.S. District, Appellate or Bankruptcy courts by the attorney's name. You'll be able to see the status of the cases the attorney has had, and what their outcomes were.
Contact the state court. Many attorneys work locally, especially those who practice family law, civil law or criminal defense law. You can ask the attorney in what jurisdiction or courthouse most of their cases are heard, and then contact the state judicial offices or go to their websites. However, the availability of such searches vary widely by state, and you can't always search by the attorney's name.