If you were planning on using the Tube today, you'd be very, very wise to find alternative arrangements. London Overground doesn't run on Boxing Day anyway, so don't think about that as an alternative. However, Bus, DLR, Tramlink and some River services will all run.
TfL have added a section to their initial press release on the services they expect to run. In a nutshell, services on all lines are extremely limited, with very reduced frequency on those lines that are running for a small part of the line. The earliest any trains start appears to be 8.30am (limited shuttle service Ealing Broadway & Acton Town on District Line) other limited services start at in the main at 9.30am.
My advice, walk, get a bus (extra buses will be provided on many bus routes particularly in the central London area) or use a Barclays Bike if you're that central.
For those who are interested, the strike over pay involves the majority of drivers asking for additional payments plus a day off lieu for working on the bank holiday. London Underground are pretty miffed by this as the staff concerned are already earning a premium in their annual salary for working on public holidays. We also have further days of strike action to look forward to in the New Year as Aslef are planning to hold three further strikes in 2012 on 16th January, 3rd and 13th February.