From London:
There are regular services that run from London Bridge and London Victoria.
From east and west:
Southern trains run along the south coast and link Brighton with Hove, Worthing and Portsmouth to the west and Lewes, Eastbourne and Hastings to the east. nationalrail.com
The M25/M23 link provides road access from London and the rest of the country. From east and west:
the A27 and the A259 provide access to Brighton. The A259 runs along Brighton seafront. Journey Planner