It depends. Although Florida has no state income tax, New York considers you working in New York if you are working remotely from home. However, if you are working from a normal business location (an office, a store, etc.) you are not receiving New York income.
In either case, you will fill out a New York Nonresident Return, and then go to the Allocation section. If you work from home, you will not need to Allocate income See this link to the Allocation form: IT-203-B (Fill-in). You will notice that on lines 1h-1j, you enter the days you worked outside of New York, but subtract the days you work from home. However, if you did not work from home, then you worked outside New York 365 days, and your New York income will be zero. You will get back all of the tax you paid in.
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