Travelling between London and Brighton is easy and painless. In London, you can travel to/from a number of different stations, including London Bridge, London Victoria and London Blackfriars. If you don't want to catch a train, there are numerous bus services operated by companies including National Express.
Depending on how much you want to pay, and which London station you want to travel to/from, your service will either be operated by First Capital Connect or Southern. A third option is to take a Gatwick Express service between London Victoria and Brighton, although this route is relatively expensive.