The easiest way to install Dropbox is to go to the Dropbox Linux page, click on the correct Dropbox binary package (they have binaries for Fedora 9, Ubuntu 8.04, as well as the source code.) If you click on the correct binary your installation system will automatically detect it and ask for your root (or sudo user) password, and install Dropbox. If you run a different distribution there are some people who are working on binary packages for them... so be patient.
Now, one of the first things you must know is that Dropbox requires the GNOME desktop. So without that installed, you will not be able to get Dropbox installed.
Once Dropbox is installed you can either log out of GNOME and log back in or you can issue the command killall nautilus and Nautilus will restart.