Determine the gross value of the estate. The estate consists of everything the deceased person owned, not just real estate. Add the fair market value of everything in the estate. For small estates, don't worry about incidentals such as ink pens, or you might estimate their combined value if there are many.
Determine whether you are responsible for paying federal estate tax on your inheritance. Estate taxes apply to the estate itself --- not the inheritor. You are liable for estate taxes only if the estate itself did not set aside money for this purpose, and only if the value of the estate exceeds the taxable threshold. In 2011, the threshold was $5 million. If the estate you inherit is worth less than that, it won't owe any tax --- although the estate executor, or you as the inheritor, must still complete and submit the federal estate tax form.
Complete and submit IRS Form 706, United States Estate (and Generation-Skipping Transfer) Tax Return. Consult with an attorney or the IRS for help filing out this form.
Take any deductions the IRS allows from the gross value of the estate. You may deduct any unpaid bills and mortgage. You may deduct the value of any portion of the estate left to charity, as well as the full administrative cost of settling the estate. If you are inheriting from a spouse, you may deduct the entire value of the estate. Any remaining value comprises the net value of the estate.
Apply the net value of the estate to your annual income, and report it on IRS Form 1040 when you do your next income tax return.
Apply any tax credits for which you qualify as a result of inheritance. Except for highly valuable estates, these tax credits usually relieve you of any extra tax burden from an inheritance.