So Zatanna uses magic all of the time, for a wide variety of purposes. Only one of her abilities is show to be latent:

Magic Detection: In canon, Zatanna is able to detect mystical force when she's in the presence of it. She can determine what the source of the power is, and get an idea of how strong the magic is. She can also recognize when two different sources have the same type of magic (i.e. she could sense the same mystical force coming from Batman and Red Tornado), so she'll be able to distinguish one magic from another.

Notably, it's not shown that this ability allows her to detect biologically-based abilities, such as Superboy's Kryptonian powers or M'gann's psychic ones. And while she can pinpoint strong enough magic from a distance, it requires use of a spell if she's not in the presence of it. Lastly, Zatanna cannot use this ability to sense if a person is something other than a human; in canon, she does not know that someone is a ghost when she encounters them.

To this end, if your character is likely to be sending off some type of magical energy on a general basis, please leave a comment to let me know?

Everything else she's shown doing requires a spoken spell along with focus and energy. As stated, she has a huge range of abilities, and she uses them frequently, from fighting villains to seasoning a turkey. Some of the ones that may affect characters directly are listed below:

1) Object Transformation: Pretty much what it says on the tin: Zatanna can turn one object into another. Usually she's showing doing this with clothing. She can cast spells that will change one outfit into another, or turn clothing into restraints (it's for crime fighting, okay?). She's also shown turning a gun into a snake and then into ropes. She can do this from a distance; there's no physical contact required.

2) Illusions: Zatanna is also able to create illusionary duplicates of individuals. These illusions appear perfectly solid, and can walk and talk on their own. They are dispelled when they are physically struck (think Naruto-clones). She can create these of herself or others, and again, does not require physical contact to do so.

3) Levitation: What it says on the tin. Zatanna can make objects or people float in the air. This is not shown to be full out flight, although she's able to make things go pretty high.

4) Blurting: Probably the big one, and the most intrusive. Zatanna is shown to have minor mind control abilities; specifically, she is able to make two separate people say information they otherwise wouldn't have. She doesn't have to know what they're going to say, as in the first instance she gets Ivo to blurt out a location the team is trying to get from him without success, but she can also make them say something specific of her choosing. Notably, this happens after Ivo states he's prepared for a psychic probe from M'gann, which again points out the difference between psychic abilities and magical ones in Zatanna's world. While no defense for this specifically is shown in canon, it's likely that a person with a strong enough magic ability would be able to resist it, as is the case with any of her spells.

Exercising this control on a character is rare, and Zatanna wouldn't do it without reason. If a thread is headed in this direction, I will contact you for permission.

This is a partial list of the abilities she uses most or can use at the present that are the most invasive. A more complete list, including what she can potentially become capable of, can be found on her application. Please feel free to comment below with any concerns or questions.