Brendan over at Untimately is having an interesting discussion on the experimentation and identification of magic items. My comment grew so long I decided to turn it into a blogpost of its own so here we are.
When I first started as a player any weapon that was given a description, even as something as common as an ornate hilt, was deemed potentially magical and it was held onto until such a thing could be determined. This mindset has transferred to my players when I took up the DM mantle. It helps that they behave as hoarders for even the most trifling of items.
As for how to determine the actual magic properties of an item this is a bit of a tough call. Josh D. is right that if you don't tell them what it is then keeping track of +1 to hit and damage can be a bit of a pain. The way I've been doing it has been to rethink how magic items, weapons specifically, work.
There are currently two magic weapons the PC's have received in my LL game. One a gift for their misdeeds, the other a trophy from defeating a bandit leader pillaging caravans and secretly employed by the master of the moathouse. For the gift, the PC was told the sword was magical but was not told in what way, only that the previous owner was glad to be rid of it. For the trophy, they liberated a jagged and unbelievably heavy axe carved out of a single rough-hewn red rock. Both of these are magical but exert no magical properties, this is how I avoid the added mental math of an additional +1 or more to attack or damage rolls.
To clarify, these weapons are magical but do not display any properties until they are activated. In the case of Sting, it would be treated as an ordinary sword until it's favored enemy (orcs/goblins) drew near in which case it would both glow and begin exhibiting the properties of ensorcelled steel (+X to hit and damage, etc.)
As for the Red Rock Axe my player's found, it is a semi-intelligent item that will not activate until its wielder has flown into a bloodrage, not necessarily a berserker or barbarian rage just a notable degree of bloodlust or battle revelry. Its now deceased wielder was an Orc Barbarian that put it good use against them after he began raging so its method of activation is not entirely difficult to discern. However, once activated the weapon craves more blood to be spilt and to be awash in the crimson life of it's masters enemies. It will provide a significant advantage (+2 hit and damage plus any effects from an intelligent item) but it comes at a price. A rather hefty one since it's current wielder, a tempered berserker, tries to keep his rages in check as best he can and with this axe he is unlikely to differentiate between friend and foe.
The other weapon, a curved sword, has been with them from the start but it's wielder possess little prowess in melee combat so it has seen little use and even fewer opportunities to activate. The sword is an ancient inquisitors sword, formerly used to hunt down apostate mages for their misdeeds. In the current age Mages do not exist but anyone with a sufficient INT or WIS can cast from a scroll, so the sword will only activate whenever it cuts into one casting a spell (clerical or arcane). Once it has been activated in such a way it becomes a +1 weapon that dispels any magical effects when it hits a target (Save negates) and prevents any further spell casting (silenced for all intents and purposes). The wielder however, is also forbidden from casting spells otherwise the sword will go dormant once more. A fail-safe built in by it's designer in case it was ever used by its prey.
These weapons do not display any magical properties because the magic imbuing them does not last forever. Their creators in ages long past designed them to lay dormant in slumber until they are needed again. For an inanimate object it may be generations until they are used again so it only makes sense that they are not firing off cosmic rays waiting for a brave soul to pick them up.
This method works very well for weapons and certain other items but it's a rather poor fit for magical armor.
One thing I forgot to mention is how Bane weapons (i.e. +1/+3 vs Lycanthropes) can grow in strength over time. This is adapted from a rule whose origin I believe is from FASA' Earthdawn game, where a weapon can become say a magic sword of undead vanquishing if you take on a quest to slay a mausoleum full of wights or a dragon slaying sword after it's been plunged into the heart of a fearsome dragon. The sword manifests the powers from the action it takes, or something to that effect.
To use the inquisitor's sword example, it may suck the magical energy out of it's victims increasing its own enchantment (+2,+3, etc.) This can become a moral quandary since the PC wielding the ever-thirsting sword may desire more power and may modify their moral outlook so that more magelings fall under their blade. Eventually becoming a twisted shell of their former self, demonizing any application of magic and becoming a scourge upon the land. Something along the lines of "You either die a hero or you live long enough to see yourself become the villain." [Harvey Dent, TDK] or Nietzsche "He who fights monsters should see to it that he himself does not become a monster."