OpenLabyrinth uses a very standard web server approach. Authors and players only need a web browser to edit and play cases.
We use a very plain vanilla Linux Apache MySQL PHP (LAMP) approach, the commonest setup for a web server. Server admins who are familiar with this approach should have little trouble in setting up OpenLabyrinth. (We have had some path glitches so we do recommend using the default paths and folder locations for least hassle.)
You can download the source code for OpenLabyrith from https://github.com/olab/Open-Labyrinth. You will find basic install notes at https://github.com/olab/Open-Labyrinth/wiki/Installing-Open-Labyrinth.
Setting up a web server may be too much of a hassle for small groups. You are welcome to ask for a free demo account to try things out to start with.
One other approach is to try a simple pre-built web server that you can run on your own laptop. We sometimes use this approach for road shows where we cannot rely on Internet access. Check out MAMP for Mac or WAMP for Windows – these are both pretty easy to set up.