This story contains both some observations about enjoyable walks you can do on your own in Lisbon and a review of my experience with Lisbon Walker. More information can be found on their website at http://www.lisbonwalker.com/.
Walking in Central Lisbon On Your Own
Despite having been built on seven hills (which makes for some steep climbs) Lisbon is an extremely enjoyable city to walk around, provided you start at the top, rather than the bottom, of the hills in question. If you keep in mind that Lisbon's historic center essentially lies in a valley that slopes down to the Tagus River, you can turn its varying elevations to your advantage by walking downhill and then taking Lisbon's efficient and inexpensive metro back uphill.
A particularly good place to start is at Parque Eduardo VII, which you can access from the Parque Metro Station, which offers excellent views over Central Lisbon's skyline. You can walk straight through its center or dawdle along the manicured hedges, but however you go you'll eventually reach the Marques de Pombal traffic circle (which has a metro station of the same name underneath it), from here you can walk down Avenida da Liberdade. The walk along the right side (as you face away from the circle) is more pleasant, but as the buildings on this side are more interesting you may prefer to walk down the left side. This terminates in Praca Pedro IV, Lisbon's main square, which is universally known as the "Rossio" and which contains a metro station of the same name. If you continue straight from here you'll pass through the Baixa, the planned center of the city that was rebuilt after the 1755 earthquake. Just beyond it (through a triumphal arch) is the Praca do Comercio, although this is currently being refurbished so you'll have to walk along the arcades at its sides to reach the Tagus which is located across Avenida Infante Dom Henrique. The Terreiro do Paco metro station is located beneath the Praca do Comercio.
The streets on the hills on either side of the city center are less orderly but are even more enjoyable to explore, provided you don't mind meandering. The Chiado and Bairro Alto are best reached by either the Baixa/Chiado Metro Station (take the Largo do Chiado exit, which is four escalators below street levels) or the trams on Gloria or Santa Justa. The Alfama is best reached via Tram 28, which can be caught either from Rua Conceicao in the Baixa or from just beyond the top of Rua Garrett in the Bairro Alto/Chiado. Get out at the Santa Luzia stop for the best views!
Walking with "Walks in Lisbon"
One of the joys of exploring Central Lisbon, and travel generally, is discovering unusual things for yourself for the first time. No matter how thorough your guidebook is, it likely won't do justice to the simultaneously majestic and slightly dilapitated feel of Central Lisbon, which feels at some times like a set for an old movie that has drifted into obscurity. However, it can help to have some guidance and for the somewhat hefty fee of €15, the company Lisbon Walker offers just that for a range of two hour walking tours. I can only comment on their Lisbon Old Town tour, which explores part of the riverfront and the Alfama, but if the cost fits in your budget I’d certainly recommend it on that basis alone. As well as the intrinsic enjoyability of the tour, the guides also dispense the kind of opinionated local advice on where to eat, go out, and drink that the tourist office doesn’t (I suppose in the interest of being fair to all the city’s establishments.) They’re also happy to answer more generally cultural questions that aren’t necessarily germane to the tour itself, something I personally find extremely helpful.
What I particularly appreciated about the tour was that unlike others that I’ve been on elsewhere, it specifically offered information that isn’t generally found in guidebooks as well as taking a more backstreets route than I would have on my own. For example, Jose, our guide, explained that when the Portuguese reconquered the city from the Moors, they targeted the Visigothic Christians for much greater persecution than the Jews or Muslims. Similarly, he noted that many of the "ruins" of the Castle of Sao Jorge (St. George) overlooking the city were actually put there in the 1940s by the Salazar dictatorship as a way to instill pride in Portugal’s glorious past. He further explained that the supposedly "medieval" Alfama actually fell victim (along with most of the rest of the city) to the 1755 Earthquake, but was rebuilt in a haphazard manner because property lines were respected there. If getting this sort of unvarnished history appeals to you, I couldn’t recommend the tour more highly, and even if it doesn’t, I’d still recommend it as it’s informative, enjoyable, and not terribly strenuous.