You can do with what you have. The other users will (in principle) need Access on their computer as well. There are viewers. Then they can not make any change. When you have many users, it would be better to put the data on the server as a back end database and link that to front ends on each computer accessing the data.
If you want to implement security rules [i.e. who may modify, update, read data], do not start with that unless you are well aware of the security model with domains, user groups etc. under Windows NT as it is basically the same concept.
Good luck