Updating WordPress « WordPress Codex

1. Get the latest WordPress zip (or tar.gz) file.
   
2. Unpack the zip file that you downloaded.
   
3. Deactivate plugins.
   
4. Delete the old wp-includes and wp-admin directories on your web host (through your FTP or shell access).
   
5. Using FTP or your shell access, upload the new wp-includes and wp-admin directories to your web host, in place of the previously deleted directories.
   
6. Upload the individual files from the new wp-content folder to your existing wp-content folder, overwriting existing files. Do NOT delete your existing wp-content folder. Do NOT delete any files or folders in your existing wp-content directory (except for the one being overwritten by new files).
   
7. Upload all new loose files from the root directory of the new version to your existing wordpress root directory.
   

Updating WordPress « WordPress Codex