I have the train times on my website at
http://www.algarvebus.info/006.htm
A taxi from Albufeira station into the old town shouldn't cost more than about 8 Euros and if there isn't one waiting phone the number posted inside the station ticket office and one will be sent.
I suggest the 1013 from Tavira with a change at Faro will get you to Albufeira at 1127. Sit on the left hand side for the best views!
(BTW, this is only four minutes between trains in Faro, so if you are twitchy about missing a connection and having to wait two hours for the next one, catch the 0913 (except Saturdays and Sundays) instead. The trains do usually wait for one another unless the delay is huge. You can have a quick wander around Faro Marina which is just down the road.)
The last train back is 2201, so you can have a really long day out if you want.
Return fare on the train is €9,60 if my reading is correct.