Getting to the ground
Of all the new grounds built in this country in the last 20 years, Brighton's is possibly the worst in terms of access and amenities. The American Express Community Stadium (or Amex Stadium for short) is around 4 miles from the town centre in Falmer, next door to the University of Sussex campus. There was obviously nowhere else that the club could possibly have obtained permission to build, because if there was the ground surely wouldn't be here.
There is absolutely no parking at the ground or in any of the roads in the area. It seems though that you can park in the streets in Coldean and Moulsecoomb, from where it's a 20-30 minute walk through Brighton Academy to the ground. You should be aware though that Moulsecoomb is a pretty rough council estate. There is limited parking at "car park B", which is a 10 minute walk from the ground. It must be booked in advance though (phone 0844 3271901), and it'll cost you either 13 or 15 quid depending on when you book. Most people understandably therefore use the train (to Falmer, next to the ground) or Park & Ride to get there. In either case it can take up to 50 minutes to get away from the ground. The good news is that use of buses and trains to and from the ground is included in the cost of your match ticket. There are three Park & Ride schemes, although only the one based at Mill Road ("Park & Ride 1") is much use for away fans.
If you're travelling by rail then you've got the option of heading for either Brighton or Lewes, and then catching the local service to Falmer. There are four trains an hour from Brighton or Lewes to Falmer, with a journey time of less than 10 minutes from either, and additional trains immediately before and after the game. There's a more frequent and slightly quicker service from Victoria to Brighton than to Lewes. However, it's likely that it's going to much quieter (and therefore quicker) travelling from/to Lewes than Brighton.

The only pub anywhere near the ground, the Swan Inn in Falmer, is strictly home fans only, as is the Hiker's Friend in Coldean. If you've driven down you'll therefore have little option other than to eat and drink in the ground. The good news is that the quality and service are supposed to be good, and they serve real ale.

If you travel down by train then there's a good selection of pubs just outside of Brighton station. Best of the bunch is possibly the Evening Star, only 2-3 minutes walk down Surrey Street. But the Lord Nelson, Prince Albert and Battle of Trafalgar are all decent enough. If you decide to travel via Lewes then I'd suggest you give the Lansdown Arms a try, or a bit further away from the station are the Kings Head and the Lewes Arms.

Pub map
Football Ground Guide
Away fans guide (from official club site)
Matchday travel YouTube video