To delete a record from the database, you will need to first locate the record. It is easiest to do this by searching the database (instructions can be found here).
After you get the listing of records that match your search query, select the record you want to delete.
Choose your desired action from the "actions" drop down above the listing of names.
If you know you are not going to need to bring this record back, choose "Delete permanently" from the listing of actions. If you don't choose this option, the data in this record can still show up in places, such as listings of contacts you've pulled from the database.
Click the "go" button.
You will be asked to confirm this deletion.
Click the "Delete Contact(s)" button.
The contact is now deleted from the database.