My daughter took Plymouth 11+ this year. It consisted of NFER Multiple Choice Maths (50 questions), Verbal Reasoning (80 questions) and an English essay to be used in case of a tie breaker. These were taken over two Saturdays in January. (VR/English 2 hours),(Maths 1 hour).
There is a mock 11+ that can be taken at DHSB in September which cost £30 and is applied for through the school PTA and is very well organised. You need to look into this about July time as it gets oversubscribed very quickly. It helped my daughter's confidence to have a 'run through' in test conditions, she only just passed the 'mock' but with her hard work and the tutor's faith she did very well in passing the real thing and will be going to DHSG in September.
I chose to have a tutor as I found it too stressful trying to do it myself as we used to end up throwing the towel in! The tutor started very slowly, every other week from April until August then weekly for 1 hour up until Christmas. My daughter peaked at just the right time as she had just about had enough of it all come December (the test was in January this year). When she first started out I wanted her to have more lessons as I naively thought the more she did the better she would become but my tutor advised against it and she was so right. Less is more sometimes!
Obviously what we did suited US and doesn't necessarily suit other people. I understand what you mean about the secrecy though as most people keep it to themselves for whatever reason it's a bit like the freemasons you can only tell 11+ parents by the grey hair and furtive fumbling in Waterstones buying as much NFER stuff as you can (although you only need the two packs!).
My daughter's teachers are vehemently against 'selective education' (unless it's their own children but that's another story!) so there was absolutely no support from her school, in fact, I could feel the daggers in my back everytime I went near the place! So in times of am I doing the right thing? this forum was fantastic although the Devon site is pretty quiet. I wish you and your daughter all the best.