You can gain a Faerie Ability by blessing your NeoPet with a bottled faerie. You can buy faeries from other Neopians shops. If you are lucky you can win one at the Tombola, or find one as a random event. You will gain the abilities in the order that they are shown below. You need to make sure that your NeoPet is at the right level to receive the next ability.
There are two ways to increase the level of your faerie Ability, one is by feeding your NeoPet certain Neggs, and another is by spinning the Wheel of Excitement.
Here are the various faerie abilities