I'm not sure if there's a by the book answer in AS&SH, but here's what we do.
If you want to identify something in the dungeon or on a mission without the identify spell, then you have to test it out somehow, if that is possible. You may end up only learning some information about an item even after testing it. A magical sword or magical armor might feel light or perfectly balanced (suggesting it is perhaps magical), but you would not learn its actual pluses or any other special powers. In the case of a magical wand, if there was a button, you would have to expend a charge to see the effect, and if it required a magical word trigger, you would be SOL. As for potions, I usually allow PCs to drink a small sip to get the gist of what they might do, but warn them that poisonous potions may have red herring effects as part of their trap-like nature. In my game, testing out items is very situational according to the item and there wouldn't be a standard answer or method for adjudicating. It is possible that in some special cases a party member might be able to discern what an item is and how an item functions because of his particular background in the game, but again, that's very situational as well. I would probably not ever use a die-rolling system, but that's just me. You have to do what works for you and your group.
If you want to identify something in town without the identify spell, you can employ a magician (or someone appropriate) who may be paid with gold, information or a favor. This method has been a good one for generating new quests for the low-level adventurers. Want to figure out how to use that wand for free? Then complete a quest for Famboozle. Otherwise, pay up.
I think I read somewhere that Gygax, at one point at least, had item identification costs subsumed into upkeep costs, so the whole process was waived and the item's properties simply revealed upon returning to town (I think he said he thought the process itself was usually less interesting than adventuring, so he didn't want to belabor it). If you wanted to know the item's properties while still in the dungeon, of course, there was still the option of using the identify spell (assuming you have it). Anyway, not sure if Jeff has commented on an upkeep cost system, but if not, it's easily grafted on.