To start with, you'll need the Everquest Titanium edition to play. No other version will do. This is because all the servers are running the same version of software, and you need to be able to communicate with the servers with the same version.
From there, how you play depends upon the level of involvement you're looking for. You can host and run a server yourself, or just play on one of the many others that are already going. So long as you have an internet connection, every EQEmu server you play on will be free. The only thing you'll wind up paying for is your ISP to connect to the internet =P
As for playing offline, you can, but you would have to host the server yourself on your own machine and then play from that same machine. This, again, depends upon your level of involvement. The setup can be a bit tedious, especially if it's your first time, but thankfully techguy84 recently wrote a very nice
PDF guide for setting up your own server.
The first step would be to get EQ Titanium, and go from there. You can usually find this in stores or online for around $20.