I have just booked flights to Bucharest for the end of August and want to travel around the country over 11 days by train, particularly taking in Transylvania with 2 or 3 days in specific places. Would apprecaite recommendations of places to visit, stay and how to tgo about arranging train journeys?

You can buy all your rail tickets at the CFR office in downtown Bucharest. When I was there they spoke very limited English if at all- a (very) basic knowledge of Romanian words for things like numbers for instance came in handy- but they were quite helpful.
I had a great experience from a Transylvanian base of Sibiu with a day trip to Corvin Castle in Hunedoara and the Roman ruins southwest of there, and a second day trip to Balea Lake with a hike from there.

Here's a plan:
Day 1: visit Bucharest
Day 2: train to Sinaia, visit Peles castle, do a cable car ride into the Bucegi mountains, catch a train on to Brasov
Days 3-5: visit Brasov, do some day trips to nearby places (Sighisoara, Harman and Prejmer churches, Rasnov fortress -all are reachable by train), then catch a train to Sibiu
Days 6-7: visit Sibiu (maybe do a day trip to the monasteries on the Olt valley) then head to Cluj;
Day 8: visit Cluj, catch the evening train to Sighetu Marmatiei in Maramures
Days 9-11: explore a couple of villages around Sighet (this part you'll have to do by bus/hitchhiking) then get the overnight train back to Bucharest
You can use CFR's (Romania's public railways) website to search timetables for most routes (here; the TIMETABLE panel on the left side of the screen) and book tickets (here; booking can be done only with up to month in advance).

Also remember that booking in advance (via official CFR website, link given by ktack above) will give you some discount on train tickets, not very essential, but still nice to travel a bit cheaper :) Plus consider that some trains in Romania are more expensive than the others, so for some short journeys there might be no need to overpay.
For some general advice would also suggest to read through this page - http://europetrainsguide.com/Countries/Romania/Romania-CFR.html