There are several rules that determine your eligibility to open a Roth IRA.
1) You must first have an income. Did you have earned income in the current tax year?
2) If you earned income, did your income exceed the limits set by the federal government? This income limit changes every year and is depends on your marital status and tax filing status to determine the maximum income. You qualify for a Roth IRA based upon your Modified Adjusted Gross Income (MAGI).
3) You cannot contribute more into a Roth IRA than you earned in income. For example, if you earned $5,000 for 2014, that is your maximum contribution.
4) The contribution limit in 2014 was $5,500 maximum.
5) There is no maximum age where you are limited or prohibited from making a contribution to a Roth IRA.
6) You are not required to take a mandatory distribution at age 70.5 like qualified IRA’s.
7) You can contribute to a Roth IRA even if you participate in a retirement plan at work.
Depending on circumstances there may be other rules but this gives you a few ideas.