Usually you can just turn up. If you are in the BMC there is a reciprocal rights agreement with the French Alpine club - lets you stay at a better rate. The BMC may be able to offer you some better advice - but I wouldn't hold my breath.
The main thing is to set off early in the morning and don't arrive at the hut after 4pm in the afternoon. If people are staying its often a 1st come 1st served basis. I have had mate who have bivied on the entrance decks to some huts in the alps, as he was always arriving late. So a bivi bag/sleeping bag/mat are useful.
Keep an eye on your gear wherever you are. A small padlock is useful - as some of the bigger huts have lockable lockers for your gear. Knowing a few phrases in the local language is always a good way of getting the hut guardian on your side.
If you are planning to buy your meals in the hut - the choices are normally take it or leave it.
They don't often make concessions for veggies either.
Hope this helps