Yes you can, provided you have some variant of UNIX installed. Eggdrop can also be run on Windows, but then that's a different story cuz eggdrop is primarily MADE to run on UNIX variants.
For now let us assume you are on linux.
Just make sure you have gcc installed, and a good enuf Internet connection.
And then simply follow the steps given on http://www.egghelp.org/setup.shtml