To make the life of admins easier, Microsoft has put together a convenient step sequence, which can be found here. It shows what needs to be done and what tools are available for this troubleshooting. Even if those tools are windows centric, the event flow is quite general and can be used for pretty much all system troubleshooting activities.
In general, it goes like:
- Check the networking [dhcp, dns, ports, firewalls, etc. ]
- Check the domain controllers [event viewer, dcdiag, resources, etc]
- Check authentication [netdiag, netsetup.log]
- Check Access control [Netdom, net view, etc.]
- Diagnosing and Troubleshooting Active Directory Problems – https://technet.microsoft.com/en-us/library/cc961826.aspx