My advice is to spend time with their online catalogues deciding exactly what you want to do in advance. If you need to consult original records, they may have to be ordered up from a store room - if you can do that in advance it will save a lot of waiting and in some cases it is essential (some records at the National Archives are stored off-site and you need to give three working days' notice).
Make a to-do list, possibly longer than you expect to achieve; make sure you take your own data with you so that you can check out new leads. Be prepared for new sources - I blundered into two unexpected and exciting new lines of research when I happened upon two books in an archive.
Allow for time being processed for a reader's ticket.
Do read the guidance on the websites too. Don't take a pen; take pencils (and not ones with built-in rubbers); take the ID you'll need; and at least in the National Archives you will not be allowed to take loose sheets of paper in with you, they must be stapled.
Hope this is helpful