I know if you make too much money you are not eligible to participate in a Roth IRA. But what do you do if you made a contribution to a Roth IRA only to find out your income is too high for you to be eligible to contribute to it?

It is considered an excess contribution to the Roth. It can be removed (along with any earnings attributable to it), or possibly recharacterized as a traditional IRA, without penalty, by the due date for filing your income tax return, including extensions). If it is not removed or recharacterized by that date, it will be subject to a 6% excise tax. The 6% excise tax is charged each year that the excess remains in your IRA. The earnings may remain in the Roth if it is not corrected by the due date for your tax return, including extensions.

...and if the individual files his/her tax return by the April 15, he/she receives an automatic 6 -months extension( to October 15) to remove the excess or recharacterize the contribution