If you’re coming from outside of Portugal your best bet is going to be to fly into Faro. From there you will need to catch the airport bus for €1.55 which can take you to the train station. From there you can catch a train to Lagos.
If you’re coming from within Portugal, bus will be your best option. The bus from Lisbon takes about four hours.
The only thing you need to worry about here is what footwear to put on. Unless you’re going out to explore the surrounding area you won’t need any transport. If you are planning to get out more, hiring a car will be your best bet.