If you have no money in pre-tax IRAs, one way to contribute to Roth IRAs without an income limit is to do a "backdoor Roth IRA contribution" -- contribute to a Traditional IRA, and the immediately convert it to a Roth IRA. The end result is the same as a regular Roth IRA contribution, except there is no income limit.
In your hypothetical situation where the person hasn't contributed yet, but is unsure whether they can directly contribute to a Roth IRA, they should just do a backdoor Roth IRA contribution, just in case. That way, it works regardless of whether his MAGI is above or below the line. There is no downside to a backdoor Roth IRA contribution (again, with the precondition that they have no money in pre-tax IRAs to begin with).
If the person has already contributed, then they should take one of the options in Dilip Sarwate's answer. Note that those options are inferior to having done a backdoor Roth IRA contribution initially, because with either of those options, gains made so far since contribution will be taxed.