I worked for H&R Block for years in the winters. The Federal stuff for one or two employees isn't that hard.
Step 1 get a Federal Employer ID Tax number. You can do this online at the IRS web site.
Step 2 When you hire an employee, have them fill out the W-4 form and the I-9 form, before they do any work for you. You can print the W-4 from the IRS website and you can Google the I-9
Step 3 Order a current copy of Federal Publication 15 . (AKA Circular E ) from the IRS website. This booklet tells you how much to withold from each paycheck. The Social Security is by a fixed percentage as is the Medicare. There are tables to figure the Federal Income tax to withould from each check based on how often you pay, how much they earn, their martial status and how many exemptions they claim.
I just print out the correct page for each employee and use it for the year.
Step 4 At the end of Mar, June, Sept and Dec. Total up the payroll info and do the IRS Form 941 for that quarter. Even if the numbers are zero you still have to fill out the form. I do it online at the IRS site and print out the copy to send in with the money.
Step 5 At the end of the year, Fill out W-2's for each employee you paid during the year. I do these online at the Social Security website. File the federal forms online and print out copies to send to the employees.
Step 6 Also at the end of the year, Do the Federal Unemployment Tax form 940. It may end up as zero tax, but work the complete form to see.
I have no experience with the state of NY but will bet the steps are pretty much the same. I did a quick search for NC dept of revenue online when I moved from VA to NC. Went to the County Clerks office to fill out the paperwork for my DBA ( registering the business name ) Then did the rest online with the state.
Quickbooks wanted $100 per year for the payroll add on. I probably spend 10 hrs per year doing the paperwork, so I figure I'm paying myself $10 per hour to do it my self. As I'm not busy full time yet, I'll keep the savings. When I'm working full time and keeping at least 1 guy busy full time, then I'll hand it over to someone else and pay them.
Rick