Here are some of the Roth IRA rules:

What is a Roth IRA?
A Roth IRA is an individual retirement plan that, except as explained in this chapter, is subject to the rules that apply to a traditional IRA. It can be either an account or an annuity. Individual retirement accounts and annuities are described in chapter 1 under How Can a Traditional IRA Be Set Up.

To be a Roth IRA, the account or annuity must be designated as a Roth IRA when it is set up. A deemed IRA can be a Roth IRA, but neither a SEP-IRA nor a SIMPLE IRA can be designated as a Roth IRA.

Unlike a traditional IRA, you cannot deduct contributions to a Roth IRA. But, if you satisfy the requirements, qualified distributions are tax free. Contributions can be made to your Roth IRA after you reach age 70½ and you can leave amounts in your Roth IRA as long as you live.

When Can a Roth IRA Be Set Up?
You can set up a Roth IRA at any time. However, the time for making contributions for any year is limited.

Can You Contribute to a Roth IRA?
Generally, you can contribute to a Roth IRA if you have taxable compensation and your modified AGI is less than:

$160,000 for married filing jointly or qualifying widow(er),

$10,000 for married filing separately and you lived with your spouse at any time during the year, and

$110,000 for single, head of household, or married filing separately and you did not live with your spouse at any time during the year.

Is there an age limit for contributions? Contributions can be made to your Roth IRA regardless of your age.

Can you contribute to a Roth IRA for your spouse? You can contribute to a Roth IRA for your spouse provided the contributions satisfy the spousal IRA limit, you file jointly, and your modified AGI is less than $160,000.

Compensation. Compensation includes wages, salaries, tips, professional fees, bonuses, and other amounts received for providing personal services. It also includes commissions, self-employment income, and taxable alimony and separate maintenance payments.

Go here for Roth IRA contribution limits.

Go here for more detailed Roth IRA rules IRS Publication 590.