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.