Brighton-bound National Express and Megabus buses depart from London's Victoria Coach Station. The trip takes about two hours. Southeastern trains leave from London's Victoria and Charing Cross stations four or five times an hour. The journey takes 75 minutes, and the trains stop at Gatwick Airport. By car from London, head to Brighton on the M23/A23. The journey should take about 1½ hours.
Brighton (and the adjacent Hove) sprawls in all directions, but the part of interest to travelers is fairly compact. None of the sights is more than a 10-minute walk from the train station. You can pick up a town map at the station. City Sightseeing has a hop-on, hop-off tour bus that leaves Brighton Pier every 20 to 30 minutes. It operates May through mid-September (plus weekends, March and April) and costs £11.