Your contact's Overview screen contains a User Defined Fields (UDF) section for the contact. Below is an example of this section:
This will display two columns - the User Defined Field that you've attached to the contact along with the specific Field Value that you've given them for that UDF.
You can add new UDFs to the record by clicking the Add link in the top right corner of the section. Right-clicking (or double-clicking) a UDF present in this section will allow you to edit the Field Value for that UDF or to delete the UDF altogether from the contact record.
You can learn more about working with UDFs here.