Here are some useful websites I've found so far for fingerloop braiding (or, more correctly, loop manipulation braiding using a finger-held method).
Website by Lois Swales & Zoe Kuhn Williams. Includes basic techniques using the A-fell method, redactions of 29 braids (some from Tollemache (15th C), some from two 17th C manuscripts), instructions for making aglets and transcriptions of 'Nature Unbowelled' (1655) and 'The Bindloss Manuscript' (early/mid 17th C).
Website by Ingrid Crickmore. Includes tutorials for numerous 3-, 4-, 5-, 6-, 7-, 8-, 9-, 10- and 11-loop braids (some from medieval Europe, some from elsewhere), plus variants on the 17th C "Spanish" braids, all using the A-fell method.
Loop-Manipulation Braiding Research & Information Centre, founded by Masako Kinoshita. Website holds all issues of their annual newsletter, detailing worldwide research into loop-manipulation braiding. An index of the newsletter issues can be found at the bottom of this page.
Website by Joanna Hobbins. Lists all of the Tollemache braids, with redacted instructions and (for the one-person braids) diagrams and examples.
Website by Cindy Myers with lots of interesting information on it. This particular page lists all the braids in the Tollemache, Harleian and Serene manuscripts, compares them and links to instructions for most of the braids.