If the receipt of the 1099 tax form does not change your income, expenses, or income tax withholding, such that they are not different than what you filed with your original tax return, then you don't really need to do anything. That is, assuming the information you previously input was accurate, and that the new information (if it were substituted instead for what you input on you original tax return) does not raise your income taxes, you do not need to amend.
In other words, if the 1099 simply confirms the numbers and dollar amounts that you already knew, then you have no need to amend your original tax return. We would recommend saving the 1099 itself, however, along with your other tax documents, for your tax records. The purpose of keeping accurate tax records, obviously, is to that you can later "prove" what you claimed on your tax return in the (usually unlikely for most people) event of an examination (audit).
Not that it is necessary in your case, but for your additional information you may want to look at this helpful TurboTax webpage (and video) on amending tax returns:
https://ttlc.intuit.com/questions/1908543-do-i-need-to-amend-my-tax-return
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