File sharing either allows you to see the 'public' folders that the remotehost user chooses for file sharing, or it also allows you to see and write to all the remote users stuff if you have the login and password for that user. If you are copying a large number of files that don't reside in one folder, or if you'd like to easily cherry pick files from one computer to put on another then this is clearly the best way. We'll talk about SSH and SCP, which are used extensively in the later instructables in this group. We'll talk about file sharing between macs Then we'll talk about screen sharing and screen sharing remotely. If you are copying files you might want to connect with either a network cable or a firewire cable. This instructable talks about connecting to your mac mini with just a network connection. I'm only going to talk about the ones I use, but they are so handy that you will probably make great use of them as well.
There are countless ways to connect and each way provides different services and are great for different things. Its the computer you generally have to connect to.
For me its generally my laptop that I use at work and I bring home. I will always use "localhost" to refer to the computer that you are connecting to your mac mini. One piece of lingo we need to set straight deals with which computer we're talking about. Connecting to your mac mini while at home or away is crucial, especially if you don't have a keyboard mouse and monitor permanently attached.