Magento prior to version 1.5 required complete access to the file system (after 1.5 an FTP client was introduced that allowed Connect access to the file system via ftp)
You can do 3 things
as above.., set all files to 777.. thisThis is a pain and you will have to reset them all after.. ifIf you have Aitoc or similar modules you will have to then track down which files need extra permissions
change the file ownership of all files to apache (or what ever your web server runs as). This is less hassle and keeps your file permissions as they were. Simply revert ownership back after the install.
Change how php runs on your server.. itIt sounds like apacheApache is running as mod_php.
mod_php
. changeChange this to fast-cgifast-cgi
and all files owned by you will be accessible to the server. Switch back afterwards to continue the benefits of mod_phpmod_php
Hope this helps