Isolate the layer
Work bottom-up or divide-and-conquer. Ping by IP to test connectivity; if that works but names fail, it's DNS. If local works but the internet doesn't, look at the gateway or a route. Prove where the packet stops before changing anything.
Use scope
Who is affected and who isn't? If one department is down but its neighbour on the same router is fine, the fault is something only that group has - a per-PC gateway, a VLAN, a duplicate IP. Scope points you straight at the difference.
Not down - just slow
Sometimes nothing is broken; a link is saturated. Monitoring shows utilization per link. A cable carrying more traffic than its capacity queues and drops packets, so everything feels slow. Find the hot link and give it more bandwidth.