Strolling in Lisbon is tiring, because there are many and steep hills close to each other. If you want to go up to Chiado (and you must, of course) a simple secret is:
Enter the Metro station of Baixa-Chiado in R. Crucifixo, go across it, and use the automatic stairs that will leave you uphill. Walking down will be easier, and Chiado is also a good location to pick tram 28.
Some districts of Lisbon are best explored on foot, as they consist of small cobbled alleyways and narrow streets. Among these districts are Alfama, Bairro Alto and Baixa Chaido.
Make sure you wear comfy shoes when wandering around these areas as many streets are cobbled and often very steep. Don't forget that Lisbon was built on seven hills.
It's nice to walk in the narrow streets of Lisbon. But the city is divided in a higher and a lower area, which makes the streets quite steep. If you are not fit to walk up and down, use the public transportation.
The Metro is efficient and fast, but you can not see the city. Use the bus or the slim, old tram to see the sights. A day ticket has costs 4 Euro and has unlimited travels on both bus, train and metro. You can also buy another tourist ticket for 16 Euro, which gives you unlimited travels on even more lines in and around Lisbon, and free entrance on museums.
Walking is one of the best ways to get around in Lisbon. It's a big city so you do have to use public transportation at times (depending on what part of the city you're visiting), but walking is the best way to explore places like the Barrio de Alfama. But remember that in historical neighbourhoods, there are a lot of hills and cobblestone streets, so wear comfortable shoes and make sure you're in good physical shape.
While in Lisbon, walk to get anywhere in the central area (Baixa, Bairro Alto, Chiado, or Alfama). Elsewhere, take the subway. It's super-clean and super-new (EU funds, perchance?) Anyway, they've named all the lines cute things like the 'Sunflower Line' and the 'Caravel line' -- it's too cute for words.
Get your legs in shape if you're planning to walk around Lisbon! This hilly city is also full of calçades, or street-stairways, that you'll be hiking up and down as you roam the older parts of town.