Exempt property means it is not subject to attachment by creditors or in a bankruptcy, which means you get to keep it. The exemptions vary by state, and you should consult a bankruptcy attorney to determine what property may be claimed exempt in Ohio. In most situations, if you wish to keep houses or cars, you simply maintain your payments as scheduled to the creditor. See more information on exemptions in the FAQ page.
The theory in Chapter 7 is that all non-exempt assets are turned over to the trustee to be liquidated for funds to distribute to creditors. In reality, however, this only occurs if the debtor does not wish to "buy back" the property. Hence, suppose a debtor has a non-exempt widget worth $1,000 which he would like to keep. Rather than sell to someone else, the trustee is normally perfectly willing to sell back to the debtor for whatever price he could obtain from a third party. The debtor may actually get a better deal because the trustee incurs no costs of sale, and in many circumstances, payments can be spread out over a short period of time.