We have more about hiring folks in our employment section. We recommend that you make sure you've covered all the legal bases for hiring someone in your state, as long as you're wondering about payroll, so you can try to avoid getting audited, sued or arrested.
Shameless plug here – payroll can be a pain in the neck, but it's super-important to get right. You might want to consider outsourcing it to an outside processor. Payroll companies can administer payroll and employment taxes on your behalf, and report, collect and deposit employment taxes with state and federal authorities. Many can also help keep employment records and handle direct deposit issues. We have partners who can help you with that.
Keep in mind, you're still on the hook, legally, for the deposit and payment of federal tax liabilities, even though the third-party is making the deposits. The IRS just wants to get paid, and they'll come after you if your payroll processor makes mistakes. The IRS “strongly suggests” that you don't change your address of record to that of your payroll service provider “as it may significantly limit the employer’s ability to be informed of tax matters involving their business.” The IRS also recommends that employers make sure their service providers use EFTPS (Electronic Federal Tax Payment System) so the employer can confirm payments made on their behalf. You can register here. 
Payroll has four steps:
Calculate the hours worked and hourly wage of your employee, giving time-and-a-half for overtime.
Calculate state and federal payroll taxes, record them, and set aside the appropriate sum in your tax account.
Calculate the employee's Medicare and Social Security taxes, the employee's withholding for health insurance and other benefits (if you offer benefits), and subtract that from the wage.
Write a check for the remainder to your employee.
It seems simple enough, doesn't it? Here's an example from the IRS.
Social Security tax rate: 6.20% + Medicare tax rate: 1.45% = Total payroll taxes - 7.65%
If an employee earns $1,000, the payroll taxes are:
Social Security tax: $62.00 + Medicare tax: $14.50 = Total payroll taxes -$76.50
The employer sends the $76.50 to the federal government.
Employees complete Form W-4, Employee's Withholding Allowance Certificate to determine how much federal income tax to withhold.
The amount of federal income tax withholding depends on the employee's marital status, the number of withholding allowances claimed by the employee, any additional amount the employee wants to withhold, and any exemptions from withholding that the employee claims.
Your bank will likely offer a direct deposit service for your business account, to help automate the payment process. If you're going to do your own payroll, you might want to consider using tax accounting software to keep track of your payments. The IRS requires payroll tax information to be retained for four years.
We have partners who can help you with that.