Last year we purchased a property. It is a private sale between the seller and us. There is a legal contract and we are making monthly payments. How do I enter this?

It depends on what type of property you bought and what you plan to do with it. If it is your personal residence,  report it the same way anyone else that bought a home and got a mortgage through the bank.  The seller "self-financed" the sale, so he/she is the mortgage holder.  He is required to send you a Form 1098 that reports the interest you paid.   If the property is your personal residence, you report the interest on Schedule A, if you itemize.  You can deduct the property tax regardless of whether or not it is your personal residence (subject to the $10,000 cap on state and local tax).  If you bought land to build a house on in the future, you cannot deduct the interest.

If it is an investment property, you can deduct the interest as investment interest on Schedule A, but only to the extent that you have investment income.  Finally, if it is raw land, you can choose to make a Section 266 Election.  Section 266 allows you to capitalize (add to your cost basis) certain expenses related to the investment property such as taxes, interest, insurance, and maintenance costs.  The election must be made each year by attaching a statement to your tax return.