As far as income tax is concerned, if you form a partnership, the partnership has to file its own Form 1065 partnership tax return, separate from your Form 1040 personal tax return. The partnership tax return includes a Schedule K-1 for each partner. Each partner has to enter information from his Schedule K-1 in his personal tax return.
You might be subject to other business taxes, besides your regular income tax, in New York. This would be true whether it's a partnership or some other form of ownership. If you hire someone as an employee you would have to deal with New York employment taxes. For at least the first year you should have a tax professional, preferably in New York, show you how to handle the taxes and prepare the tax returns for the business.
There are other considerations that you have to pay attention to besides taxes. You should consult a small-business lawyer in New York for advice on how to set up the business. And consult an accountant (who might also be your tax expert) to show you how to keep financial records for the business.
