This can be accomplished by running a central OpenLDAP server and configuring the machines to use the LDAP server to authenticate users rather than local /etc/passwd-based unix account authentication.
I'd rate the level of skill required to get it working properly and troubleshoot the problems and issues that come up as "medium-high" to "high".
If you are already an LDAP or MS ActiveDirectory wizard or guru, it will be straightforward. If not, be prepared to learn the underlying pre-requisites.
A few pre-requisites to implementing multi-machine LDAP login:
Must know how to install, manage, configure and use LDAP.
Ability to troubleshoot linux systems, and isolate general symptoms back to root-cause(s), then integrating LDAP expertise to identify and make the fix.
Word of Caution
A single-server implementation of LDAP for unix authentication introduces a new single point of failure into the machines on the network:
Anytime the LDAP server goes offline or becomes unavailable, it will not be possible to login to the linux machines.
Additional Reading and Tutorials
General enough to be useful for other linux distros:
pam_ldap- and nss_ldap- oriented resources:
(NOTE: no longer best practices [see discussion below], but may still be informative)