How do I connect my MS Access database to the LAN?
There is nothing magical about this.  Just put the Access database file in a file share on your LAN and let people access it from whatever computer they are using.

If you will need to be sure to open the database in shared mode.  Go to the options, select client settings, advanced, and set the default open mode to "shared".  (Depending on your version of access, the way to get to this setting may vary.)

You can do something more elaborate, like segregating your data and your GUI and joining the front end databases to the back end with linked tables, but that may well be overkill.