I moved under a month ago. While I'm not planning on staying here permanently, I'm not a dependent, so I assume I need to declare residency somehow. When do I need to file for residency? I saw something that says NY doesn't consider you a resident until you've lived there for 90 days?
If you are still living in NY at the end of the year AND you have worked in both states you will file a part year return in each state. Make sure to check the NY state requirements on changing your DL ... most require it within a certain time frame after moving and check with your auto insurance as well.
Here is a link to New York State's definitions of resident and nonresident for income tax purposes. Note that you do not "declare" your residency. You are a New York resident if you meet the definition of a resident.
"While I'm not planning on staying here permanently..."
If you're in NY temporarily in order to attend school, and you intend to return to your home in Wisconsin, then for tax purposes you remain a resident of Wisconsin. In tax terminology, WI would still be your domicile state, and ALL your income would be taxable by WI. Any income you would earn by working in NY would also be taxable by NY. In this scenario you would file both a non-resident NY tax return reporting your NY income and a resident WI return reporting all your income, including that from NY.
But if you've abandoned your WI domicile and do not intend to return, and you've made NY your new main, primary home, then you became a domicile resident of NY (and ceased being a resident of WI) when you began living in your new NY home. In this scenario you would file as a part-year resident of each of the two states. See What is domicile? on page 3 of this reference for further explanation:
Finally, even if you intend to return to WI, if you "maintain a permanent place of abode in New York State for substantially all of the taxable year and spend 184 days or more in New York State during the taxable year, whether or not you are domiciled in New York State for any portion of the taxable year", NY will consider you a NY resident for tax purposes - making all your income taxable by NY. An example of a "permanent place of abode" would be a rented apartment. A college dorm is not a permanent place of abode.
Note that, since Wisconsin and New York define residence differently, it is possible to be considered a resident of both states at the same time. You can have only one domicile, but you can have more than one residence. As TomD8 pointed out, if your domicile is in Wisconsin, Wisconsin considers you a resident, but you might still meet New York's definition of a resident, even though your domicile is not in New York.