I donated my eggs and was wondering how much I would need to pay taxes on the services rendered? I am married and live in Washington state

The bad news it is taxable income.  The good news is that it is not considered "self-employment" (for providing a service) so you don't owe self-employment tax.  You should expect to receive a 1099-MISC with the income in box 3.  Enter the 1099-MISC and answer the questions in the direction away from the idea of performing work -- this is not similar to your usual job, you did not intend to earn money, you do not plan to do it again.  There may also be a box to check on a page of Special Circumstances for "this was payment for a medical study."

The income will end up as 'other income' on line 21 of form 1040.  It gets added to your other income and taxed at your regular rate (15% or 25% for most people).