Mine tips about traveling in Lisbon.
I have been many times in Lisbon and find it easy to travel around the city and visit my favorite spots. The subway (Metro) works fine, buses and trams do it too. If you wish to visit the coast line all the way to Cascais or Sintra take the trains for those destinations from some of the stations they pass by.
1. Buying subway tickets
As soon as you get out the airport exit doors, turn right and walk until you see a Metro sign.
You will see the tickets machines lined up to one of the walls. Sometimes there's a queue line, please respect that.
First you have to buy the subway card and then you have to fill it with tickets. Chose the kind of tickets that suits you best (one travel, a full day, week, and so on). There are several zones too, check them here.
The subway card expires only after one year from the day you buy it, so save it! Maybe you can givit away to someone else traveling to Lisbon. Or, maybe you have an excuse to travel to Lisbon soon again :-)
2. Mosteiro dos Jerónimos
So... One of the main turist attractions in Lisbon is the Mosteiro dos Jerónimos. The tickets queue is usually painful to watch, specially on hot Summer days. But what many do not know is that right beside the Mosteiro dos Jerónimos you can find the Museu Nacional de Arqueologia, there you can buy a "two in one" ticket and visit both places and there is almost never a queue there. Actually the Museu Nacional de Arqueologia is an hidden gem in Lisbon with a smal but wonderful permanent exposition on egyptian, roman, celt and other culture's artifacts. Totally worth a visit before you take the great quest that is visiting the enormous Mosteiro dos Jerónimos.
3. Chose your cup of tea but indulge yourself time for surprises
There are loads of thing you can do, see, eat and experience in Lisbon. Many may be fun for you and many may not be quite your cup of tea... Do your homework, chose carefully what you want to see and do, most important if you only have a few days to visit the city. For example I almost never go to Bairro Alto, the music and ambience there may be loved by many, but it is just not my thing, so I chose to spend more time in other places, for example the Museu de Arte Antiga. Search for your interests but leave some time for surprises. Ask a local about their favorite spot in the city and visit it and it may be a really nice surprise that you can't find in a travel guide. :-)