Select them and them use the delete button of your choice. There is a delete button on the Address Book toolbar. You can right click and select Delete. The delete key on your keyboard works.

((I cannot access my address list

It would help it you provided some details when asking a question. We cannot see your computer screen and are not mind readers. You ask about deleting a few contacts and now your entire address book is missing.

What is preventing you from getting to your address book? Do you have the Mail Toolbar showing with Get Mail-Write-Address Book etc on it?

If not press the alt key to make the Menu Bar appear and select View-Toolbars and turn the missing toolbars back on.

Address Book button is on the Mail Toolbar.

Open Address Book, and if you don't see Personal Address Book and Collected Addresses in the left pane, select View/Layout/Directory Pane; press Alt if the Menu Bar is hidden.

Or, open a Write window, press F9, then select a contact in the Contacts sidebar, right-click, Delete.

When I bring up my address book, only 1 name appears on the screen. I can't find all the names that I had in my address book.

Are you sure you are viewing the correct address book. By default Thunderbird has 2. The Personal Address Book and the Collected.

sfhowes provided the instructions for turning on the Directory Pane in the Address Book window. Turn that on if it is not already and check your other address books.

It could be that you don't see all the names because you imported contacts from another program, and the First and Last fields are empty. Try View/Show Name As/Display Name.