All good advice pointing to information in
@Kevin frazier 's post. I'll only add that
if you haven't already replaced the stock air filter system NOW is the time to do it. Beyond the performance enhancement you'll have opened up room to do future maintenance AND you do not want to try to put that stock contraption back together. You'll know that once you start taking it off. RamAir or K&Ns.
Maybe this is obvious, but you'll want the tool for lining up the cams if you end up replacing shims. I think I saw on here recently that someone was making them. You may (?) be able to reuse the gasket. I'd have a new one on hand along with the gaskets that go under the bolts that hold the cover on and a dab of gasket sealant.
If you need a shim you'll have hit the jackpot if your local Triumph dealer has what you need- none of them carry them. Order and wait. Some early (80s - 90s) Hondas and Yamahas use the same 25mm size. You may be able to find them from their dealers.
In my experience if you don't plan ahead and have parts ready to go before you tear in, this routine job can go for weeks waiting on parts.