During the magic phase spells may be cast. Some magic items also enable characters to cast spells. The Warhammer Magic supplement describes many more magic items and further types of spell, but all work in fundamentally the same way.
Magic items which can cast spells are clearly marked 'SPELL'. If you look at the magic item cards you will four cards marked in his way: the Horn of Urgok, the Claw, the Doomfire Ring and the Staff of Lightning. These items contain spells which can be cast in the magic phase.
Most magic items can be used by any heroic character, not just by wizards, but they cannot be used by ordinary troops. Some magic items can only be used by wizards, or by characters of a specific race. This is indicated on the card for the item.
As with the hand-to-hand combat phase both players participate in the magic phase. Both sides are allowed to cast spells using their spell cards. A spell can only be cast once per magic phase. Some spells can be cast every magic phase, others can only be used a limited number of times, as indicated on the card.
The player whose turn it is begins the magic phase by choosing one of his spell cards and casting it. The card is placed face up on the table and the player reads out the effect. Once the spell has been resolved his opponent chooses and casts one of his spells in the same way. After both sides have cast a spell it is the first side's turn again, then his opponent, and so on. Spell casting alternates in this way first one side, then the other, until neither side has any spells left to cast. As there are only four spell cards provided in the Warhammer game itself, spell casting will be relatively brief, but you can imagine how with many spells to play casting might alternate in this way for quite a time as wizards cast spells against each other and on the various fighting troops. Once all spells that the players wish to cast have been cast the magic phase is over.
Rules for the spells themselves are given on the cards which describe them. Note that in the case of the Staff of Lightning you must make a test when you use the item to see if its store of energy is used up by the blast. This means that although you know the staff will work at least once, you can never be too sure if it will work again, so you must be careful not to waste its magic against a weak or trivial target.
There is nothing to prevent a single hero or wizard model having several magic items or using them in the magic phase. If a model is slain then any magic items it has are assumed to be either destroyed or rendered inactive. Of course you might choose to invent a game where players strive to capture and recapture a magic item, and it passes from one side to the other as each tries to control it. This would make a very entertaining game, and obviously you would want the item to be taken from slain individuals and used by others. However, in the normal run of things magic items are assumed to leave the game with the death of their users.