mmyk72. Now it has been about three years but this is what we did.
First we did not take the train or bus from Lisbon, we drove from the coast. So someone might jump in here to tell you the best way when coming from Lisbon.
We parked near the train station and took the #433 bus to Sintra- Vila where the main tourist attractions are. The bus runs to Sintra-Vila to Castelo Mouros, Palacio da Pena and back quite regularly.
If you have good legs and stamina you can walk it. I opted for the bus.

Thank you so much for all the info! This is GREAT! We've found an apartment in the Baixa area. It has a small balcony with views on the river and town. Looks great.

Ireynold1 - I'm going to print off your walking tour and take it with me. Thanks for that link.

Sher, thanks again -You've been great!