The plan is to build an app based around a database and have it run on a server. People will then use, mac, pc, linux, or mobile devices to access the server app, mainly to pull information from the database or add to the database. I have never done any networking, could you help direct me in the right direction. Also, would I be better off just building an app that is just a database that is accessed from another app that can be written for all other systems?

Is the database going to be on a LAN? If yes, then your job is quite easy -- there is not much difference connecting to a databse on a LAN then there is connecting to the database on the local computer. Just put the server's IP address in the connection string, all the reset is the same. If the server computer is running a firewall you might have to configure the firewall to allow incoming connection requests, but that isn't a programming problem.