Is it a black "flip key" or a red "fixed blade" key?
If it's the black key, the battery is held in a little tray on the side of the key. You just need to turn the screw-like lock visible when you flip the key open to the unlocked position and the battery tray will pop out. Replace battery (taking care to have the polarity correct) and "lock" it again.
If it's the red key, you need to lever the two halves of the key open at the little notch near the Alfa logo. Then you will see the battery, which you can replace and then just push the two halves of the key back together again.
In both cases, make sure you don't lose the immobiliser chip. It's a little piece of black or grey plastic, completely separate from the circuitry of the key and it is easy to lose. If you lose it, you're screwed.