Absolutely.  Setting up a LAN is a bit beyond the scope of this venue but certainly possible.  Personally I recommend a wired solution but I'm old school and grew up in an era where wireless wasn't reliable.

That said you are going to want a computer that is always on so it is available to everyone. I don't allow mine to sleep or hibernate.  That will be the machine you designate as your "Server".
See the Split Your Database video.  
I recommend not using that computer for actual production though you could.  Just make sure to use your own FrontEnd on each computer.
Also see the Relink Tables.  You will need to have a good knowledge of that for when you do any updates to the program.

Hi Cathy, it actually costs more to host your own database on a LAN -- you need a PC dedicated to it, you need to maintain that PC (upgrades, repairs, etc.), you need a room to put it in, you need to use extra electricity 24/7/365, you need to consider security, etc., you get the picture; it's practically a second job if you do it on your own PC.  But if you put your database on an online hosting service like Winhost (which costs as little as $5 a month), that eliminates a lot of that headache.  But to use Winhost, you have to use SQL Server, or anything that can actually run on the Internet, because Access can't.  And you need fast Internet connection too.

Richard runs his business on a dedicated PC in his office, but I don't recommend anyone doing that unless you can afford to hire someone with Richard's technical skills, or possess his skills.