There will be no problems having more than one concurrent user updating
the database at once. Access employs various record locking techniques
to ensure that users cause minimal disturbance to eachother's work.

In the senario you described, a seperate instance of the database file
will be opened on each computer. As users open a record for editing it
becomes locked. Only one version of the information in the record can
be saved at a time. If there is a conflict, then depending on the
conflict type - a user will be presented with a message box asking for
confirmation on whether they want to take over the other persons work.

In the database options you can fine tune the nature of the record
locking - but I recommend leaving the defaults.

If you are planning to expand the user base, it might be a sensible
idea to split the database into front ends and a backend - but that's
another topic for another post.