Lisbon's Aeroporto da Portela is Portugal's largest, and the main hub for the national airline TAP (Air Portugal), as well as offering routes on budget carriers such as Vueling into Spain and Easyjet to the UK (some routes are seasonal). To check out which is your best option of flying to Lisbon, visit Skyscanner.
Alternative options if you can't fly direct to Lisbon would be to fly to one of the other major airports in the country, such as Porto to the north or Faro to the south, and travel internally. Given its central location in the country, Lisbon is not too far from either (a couple of hours' drive, or train ride), so this may be an alternative if you find all flights into the city fully booked, or prohibitively expensive.
By Train
If you're travelling from elsewhere in Portugal, then you'll need a good way of finding out times and information, such as the Portuguese Railways Website (in English). Such a handy link. Failing that, there's also Rail Europe, who are particularly good at this sort of thing.
As a rough estimate of times, the fastest trains from Porto and Faro to Lisbon take around 3 hours, the slowest (stopping services) can take more than 4 hours. Naturally the quicker (Alfa Pendular) trains are more expensive, but good deals can be found booking in advance.
