Magic Items Are Special
Create a 3x5 note card for each item to give to the lucky new owner (keep a separate card or notebook for secrets about the item the player has not learned yet). Providing something tangible that the player receives, can hold, point to, wave in the air, throw across the room when it fails, and is missed when taken away is a bit of psychological trickery. But trickery that, from personal experience, creates heaps of fun. Unfortunately, it takes no small effort esp if like me you draw pictures too.
The card provides space for descriptions, pictures, history and the like. Occasional additions to or outright replacement of the card should be made as the player discovers the item's secrets. Reserve the back of the card for player notes; where they keep it, thoughts on how it works, great deeds accomplished with it, whatever. In manager speak you want to facilitate player "ownership."
Never flat out tell the player what an item does. Do not include mechanics in your descriptions. Never out loud for the whole group to hear, provide them privately. Allow the owner an opportunity to roleplay item's explanation and usage. The same way scary movies slowly hint at what's so scary the mysteries of magical items should be slowly revealed. Provide one detail in an epic floor-to-ceiling mural, another in a bard's song several sessions later.
Even if you want the players to know everything upfront don't just blurt out "It's a Horn of Blasting, can demolish doors, walls, small structures and does 6d6 to constructs." At the very least say in your best fabulous voice "Aha! You have found the legendary Trumpet of Droog. A single note of which shattered the stone guardians of Thool. A sustained blast from this legendary horn will crack and crumble city walls and utterly demolish lesser structures." Pass the game mechanics to the owner in a note, or hey on that 3x5 card you made for this item.
Some rules expect there to be plenty of accessible "plus items". Which really makes it hard to maintain the mystic of magic. Solution; items that only provide a plus bonus aren't magical! They are legendary masterworks. "You, lucky sir, hold a Montoya Blade forged more than 300 years ago when the Golden Caliphs still ruled." You could keep them magical and do the same thing. But, +1 hit/damage seems like the effect of a master craftsman. Something magical should be so much more...
Magic Items Are Unique
When describing an item describe that particular individual item. Describe in specifics, don't neglect sounds, tastes and smells the item possesses or generates. Depending on how magic & morality work in your world there might be other detectable emanations. "Before you is a 5' long smooth metal staff capped on one end by a large translucent bluish-white crystal. It crackles with arcane power." Not "Found a Staff of lighting, they are from 5-6 feet long and often have crystals incorporated in their construction."
Focus on one or two signature details. Not just "a crystal" but "a large translucent bluish-white crystal." Consider making items other than scrolls and potions literally unique. It's pretty awesome to know there is exactly one Rod of Lordly Might and your character gots it. If a player asks a leading question "What's in the crystal?" Roll with it! "The multi-faceted crystal captures your attention. Within its depths the torchlight's feeble orange light is reflected and amplified into the purest white. You drift off into pleasant memories of moonlight sparkling off the frost white snows of your long missed homeland." Maybe that's too fluffy... but, hopefully you get the idea.
Getting your players accustomed to specific traits being associated with particular magics creates opportunities for atmosphere and immersion. From frequent past usage everyone knows that invisibility potions smell strongly of lemon. While in the Dungeon of Dark Despair the scout makes a detect hidden check. Instead of blurting out "There's an invisible bugbear behind you." Lean forward, sniff the air and whisper "Something familiar, a smell you can't quite place. It gets stronger, you know this smell. It's lemon! From behind you and quite close."
Magic Items Are Important
Once a player has the item, don't let them forget about it. Reinforce how rare, magical and amazing it is. Peasants, followers, and hanger-ons will beg to see it. Collectors will offer to buy or try to steal it. The characters will hear songs that mention it. Perhaps the heir of the original owner believes it rightly belongs to them and takes their claim to the authorities. Does it need maintenance? Perhaps a magical fungus starts growing on it. "Brave sir Hadley what is that fuzzy brown stuff on your Holy Avenger?".
If they carry it on their person it should be in danger; of being broken, getting rained on, pick pocketed, drained of magic, dropped into a volcano. Players keeps it safely stored "at home"? The place should be broken into and ransacked but the item was fortunately not stolen, this time! Let them overhear how a great conflagration burnt down the characters home town. Make them fret over whether or not their hoard is so much melted junk. If it fits the character, encourage them to roleplay misplacing it for a few days "Oh, here it is, in my other robes."
Don't make every event negative. It shouldn't be a constant burden just to own a magic item. Positive encounters persist even longer in players' memories. An artist or sculptor might desire to see it, even pay for the privilege. Perhaps a great wizard asks to study it. Having a wizard owe you a favor should be worth something. Events involving the characters' magic items shouldn't come up every five minutes either. Occasionally when you need a plot pick up or if the players complain about there not being enough phat lootz.
sirlarkens mentioned the "It's Sort of Like a Wand" article from Dragon Magazine. Looking it up I'm damn sure that some 19 yrs ago this is the article that got me started. Garry Coppa, where ever you are, I owe big. More recently I've gleamed sage advice from the most excellent Roleplaying Tips newsletter. Oh hey, look what they have done there.
I challenge every DM to make it a personal goal that every magic item your players pry out of you will be notable and prized by the character who obtains it. Invest as much time detailing items as you do on NPCs. Give them names, colorful descriptions, histories, previous owners, secrets. Make them mystical, wondrous, and exciting. It is likely that characters will have more interaction and a longer relationship with their items than they will have with most NPCs.