In general, please remember to include the specific command you are running. When you say "I am unable to install drupal" we have no way of knowing what you are doing and if you are doing it correctly.
So, what you are describing is a classic permissions issue. On Linux, you can only install things as root. If you are trying to install from source and you have already ran its configure script and compiled it using make, you should now run make install as root.
If you are following (as you should) Fedora's HOWTO and installing through yum, make sure you are running yum as root.
In any case, it is a VERY bad idea to have /var/www globally writeable (777). That opens a world of security problems.
Finally, as a general note, if you want to have read/write access to a directory called /foo/bar/baz, it is not enough to do chmod 777 /foo/bar/baz. That will give you access to the baz directory, but you still don't have access to /foo/bar so it will make no difference. It is kind of like unlocking the door to your bathroom but not the front door of the house, the bathroom is theoretically accessible but you can't get into the house so it makes no difference. What you need to do is change permissions for your target directory and every one above it. You can do this with the -R switch:
chmod -R 744 /foo/ This will set the permissions for /foo and all its subdirectories. However, I repeat, do not do this for the /var/www directory, it is a serious security risk.