Normally, the IRS doesn't need proof that you received an inheritance. The executor of the estate submits a form to the IRS that lists the amount given to each beneficiary. Only in the event of an audit, or if questions arise because the amount you listed as having come from the estate differs from the executor's listed amount, would you be asked to submit proof of the amount received and from whom. Doing so is a fairly simple and straightforward process.
Find any documentation you have regarding the inheritance you received. This can include items such as a copy of the will and any correspondence you have from the executor of the estate.
Contact the executor of the estate if you don't have any documentation about the inheritance. Ask the executor to provide you with a letter detailing the amount of the inheritance and the date it was disbursed to you. You may also want to have the executor state the way it was disbursed to you -- whether it was via check, money order or some other means. Have the executor provide you with the estate's tax identification number.
Obtain a copy of your bank statement showing your deposit of the inheritance.
Make a copy of all the documents and send to the IRS, in care of the person and department that requested proof of the inheritance. Make sure to send the copies, not the originals, because there is always a chance the IRS will lose them. Also be sure to send the documents as certified mail, which will prove that the IRS received them.
In an audit, the IRS can request multiple years of tax returns, so be prepared and gather documentation for your previous returns.