In The Lord of the Rings, Gandalf notably loses his staff to Saruman. But he has it back later (notably after The Fellowship leaves Rivendell & enters the Mines of Moria, where he uses it to light their way).
I haven't seen 'the extended version'; does it show him using his Maia powers to manifest a new staff? or did he get it some other way?
I do not believe the extended version shows us how, but the staff taken by Saruman is different from the one used until he falls into the chasm in Moria.
(Links rather than embedded because I'm not sure of the licensing of the photos)
You can clearly tell from the photos that although they are both rough wooden staffs, the shape of the head is very different. The Moria staff is more open at the top, and he places a crystal there which he uses for light.
I think we can therefore presume that he made or was gifted a new staff.
Gandalf never lost his staff in the book. However, Gandalf later destroyed his staff in Moria while facing the Balrog in the chasm and subsequently after. After being restored to life he was taken to Lorien where Galadriel and the Elves gave him new clothing and apparently a new staff (Hence why he's wearing white robes).
In the movie he receives Several Replacements, Presumably the staff is just a stick, used as a conjuring tool, a conduit of power. Notice in the movies Gandalf uses no abilities of Magic without his staff rarely.
