Who can use wands, rods, and staves?

Scrolls - 3.5e DMG pg 238. You must have deciphered the writing on the scroll (a spellcraft check DC20+spell level or use of read magic), then for the spell to work you must be able to cast the correct type of spell (arcane or divine). The user must have the spell on his spell list.

Rods - anyone can use a rod (DMG 3.5e pg 233)

Scrolls - 3.5e DMG pg 238. You must have deciphered the writing on the scroll (a spellcraft check DC20+spell level or use of read magic), then for the spell to work you must be able to cast the correct type of spell (arcane or divine). The user must have the spell on his spell list. The user must also have the minimum ability score (eg a 15 in the correct ability to cast a 5th level scroll). Finally, you must have a caster level equal or higher than the scroll's caster level. If you don't, you make a caster level check to cast the spell.

Staff - 3.5e DMG pg 243 and 213. If you have the spell stored in the staff on your spell list (even if you can't cast it yet) then you can use the staff. Note that the DC's for staffs are worked out using your own ability scores and feats, and even your own caster level if it's higher than the caster level of the staff. This is what makes staffs such good choices in 3.5e.

Wand - same as for staffs. I've just noticed that it says you can use wands whilst grappled, which is interesting.

Hope this all helps, and I haven't made any really stupid errors. :D

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