The Red Tram passes through Martim Moniz, Graça, Portas do sol, Sé (cathedral), Conceição, Chiado (Camoens), Estrela and finishes its stroll in the Place du Commerce.

Some things worth knowing:

1) Don’t buy tickets onboard. The tickets sold for cash onboard are basically tourist traps – you pay a lot extra.
2) Instead, buy a smart card from any Metro machine. There is a 50 cent charge for the card, and you then pre-load it with journeys. When boarding a tram or funicular. simply hold the smart card against the reader. This validates your journey. I think each journey is about 1.20 Euros while buying it on board is in the 3 Euro price range.
3) If you do a hop-on, hop-off sightseeing tour, those offered by the Yellow Company include public transport on all the regular trams and funiculars for the duration of the ticket (48 hours, I think), as the Yellow Tours are run by the same company as the bus & tram network. WARNING: they do not apply to metros or commuter trains, as I found out when taking one of the latter…