If you're only working for yourself at home, then you're a sole proprietor. There are a couple of resources available. Firstly, here's the New York State Tax Guide for New Businesses. It details which form you're supposed to be filling in:
A sole proprietorship is a business owned and operated by one person
(a sole proprietor). This is the simplest and most common form of
small business organization. Sole proprietors must report their
business profits or losses on their federal and New York State
personal income tax returns.
• If you are a full-year New York State resident, use Form IT-201,
Resident Income Tax Return.
• If you are a nonresident or part-year resident of New York State who
has income from New York sources, use Form IT-203, Nonresident and
Part-Year Resident Income Tax Return.
• If you expect to owe New York State, New York City, or Yonkers
income tax when you file your personal income tax return, you may be
required to make estimated tax payments during the year. For more
information, see the Tax Department Web site, Form IT-2105, Estimated
Income Tax Payment Voucher for Individuals, and the instructions for
It also details important info about tax year dates, how to need to keep your books, how long to keep your records for, and other information that you may need to read. I definitely recommend familiarising yourself with this document.
As far as deductions are concerned, usually every year a document is released as a tax guide for the year. For example, this is the 2013 IRS guide for Business Use of Your Home.
It details how to determine if you qualify for deductions, here's a handy flowchart from page 5:
And also mentions which deductions are allowed. Here's a table from page 7 breaking down expense types and if they qualify:
The document also contains details of deduction limits, how to calculate partial deductions and other important information too detailed to describe here. It is absolutely necessary to read this document to ensure that the law is complied with.
Doing your taxes for your business by yourself can be a hairy experience in the beginning and does require a significant amount of reading and digging through government websites, but it can be done. US taxpayers can call the free hotline numbers detailed here for help. I've copied the most useful three line details below:
800-829-1040 : IRS Tax Help Line for Individuals
800-829-4933 : Business and Specialty Tax Line (new)
800-829-3676 : Forms and Publications