There are five main airports which are good for Brighton
I've sketched out the train links through London for the major airports below - I've had to miss off a lot of other possible routes (especially on the underground) to get the diagram this simple, so do not feel you need to take any of the routes illustrated.
There is also a small airport on the outskirts of Brighton (Shoreham airport) but I don't know anyone who's ever flown from there. The place to go if you've got a private jet though ;)
Once you get to Brighton, there are taxi ranks outside both the train station and the coach station, so getting on from there won't be too hard. They are both a short walk from the centre of town and near the main bus routes, should you feel like a wander.
I'm not sure on the various ferry ports to the country, but once you are here you can get free route information from the AA website (Automobile Association that is!). This will give you a map of a good route and list of the major traffic blackspots.
If you are travelling around the M25 (the circular motorway around London), it's worth knowing that the eastern crossing of the Thames at Dartford has a toll (£1 for a car I think), so it's probably worth getting some pound coins beforehand if that's on your route.
Also the M25 itself is a very busy motorway (especially during rush hour), so be prepared for delays there. The M23 (the motorway from London south towards Brighton) is usually pretty smooth unless there's an accident.
Things get a lot more complicated once you get into Brighton (the one-way system is pretty mad) but I'll talk a bit about that later.
I've mentioned a bit about this already, but there are two main routes to Brighton from London and routes along the coast to the east and west (there are of course other routes but these are the most frequent).
The nicest route from London goes from London Victoria to Brighton. Trains leave for Brighton every half hour, taking about an hour to get down to Brighton. Because Victoria is a terminus it's easier to get a seat on one of the waiting trains too. The first train to Brighton leaves about 4am in the morning, and the last one is about 1am at night.
The other (main) route from London is the First Capital Connect (formerly thameslink) train service, that runs from Bedford through the middle of London down to Brighton. Once the train gets to East Croydon (in south London) it follows the same route as the Victoria train. They run every half hour as well, and link up with the following underground stations
Farringdon has the shortest walk from tube to train, so is a good bet if you are coming in from Stansted. Also the St Pancras International station only opened up in December and I've not yet been there to see how easy it is to change - there will definitely be a bit of a walk but I'm not sure if you'll need to go through the ticket barriers.
On a more mundane note, the First Capital Connect trains are a couple of quid cheaper than the Victoria trains, but can be busier and the seats aren't as comfy.
The full London tube map is here, but unless you are in a hurry the Circle line will cover most of the stations you might want to take to get to Brighton. The Piccadilly line is the cheapest way of getting to and from Heathrow, and the Jubilee line is the fastest line for getting from the east of London to the west.
West from Brighton is a train line that goes to Worthing, Portsmouth and Southampton. These trains are usually slow though, so the quickest route from Wales and the west of England is via London.
East of Brighton is the line to Eastbourne and Hastings. There is a train from Newhaven harbour (which runs ferry services to Dieppe and elsewhere), but there are also trains that travel on from Hastings station to Ashford Internation train station, which is on the Eurostar line (from the Channel Tunnel).
If you are coming into the country by train, you have the choice of stepping off the Eurostar at Ashford and taking the slow (but scenic) route via Hastings or going to London and taking on of the London lines down to Brighton. I've not travelled on the Eurostar since the new station at St. Pancras opened, but it is right next to Kings Cross Station and lots of different tube lines converge there. I'm not sure of the best route there, but via London is probably quicker if you can handle the crowds.
Also there is a Virgin train that runs from Glasgow via Manchester, Birmingham and Reading (and the outskirts of London) down to Brighton, and this is probably the simplest way to get to Brighton by train from Scotland and the northwest of England.
You can get train times for all these routes from the National Rail website. If you are travelling on the weekends, there may be engineering works (which probably won't show up on the site). If so there will be a replacement bus service from the front of the train station. Usually the replacement bus is faster than the alternate route that the trains might take (if you get the option that is).
Finally train tickets for routes north or west of London are expensive but can be dramatically cheaper if you buy them a week or a month in advance. Trains to and from Brighton to the London area don't have this (it isn't even possible to reserve seats on the Brighton lines), so can be bought on the day for the same price. The Virgin trains up to Manchester and Glasgow do offer reservations I believe.
There is a website that sells train tickets on-line, called The Train Line. The site also claims to allow collection of your tickets from the "Quick Ticket" machines around the train stations - you will need to have your credit card and the booking number to make use of them, but I'm not sure which cards are accepted (Visa is certainly accepted though). I don't know if the Trainline site delivers physical tickets internationally.
As well as the local bus services, there is a National Express coach station in the middle of Brighton.
Most of these travel up to Victoria Coach Station (10mins walk from Victoria train station), which is a major hub for the coach network, and where you would catch onbound services to (or from) the rest of the country.
As mentioned before there is also a direct coach service to Gatwick and Heathrow airports (coach number 747), stopping at
Coaches are cheaper than trains, though obviously less comfortable. You can check fares and times at the National Express website (though again I'm not sure about ticket collection/delivery for international travellers). For the airport route at least there isn't any saving for booking in advance, though there may be for other routes.
