I just upgraded from 1.5 to 126.96.36.199. I was terrified at having/making a mistake and completely deleting everything. As some others here have said, it is scary reading delete all files. I also could not figure out how to back up my database.
I followed the threads and installed 'one click backup'. And then I ftp'ed a copy of all my files wordpress files to my HD. That was my fail safe, I could reupload them if the worst happened.
I then proceded with the upgrade as per the codex instructions. I deleted everything except 'wp-config.php' and the FOLDER 'wp-content'. Uploaded all the new files EXCEPT 'wp-config.php' and the FOLDER 'wp-content'.
I followed the directions, and they were correct. I went to the upgrade url specified, and I was done. Everything is working that I can see.
Good job developers.
Thank you for the clear and precise help/instructions.
And to the fellow newbies, take it slow and everything will be fine. Always, always have a copy/duplicate/backup just in case.