How would you troubleshoot a server or network that users report as slow?

Work methodically from the symptom outwards rather than guessing.

First, define the problem precisely: who is affected, since when, is it one application or everything, one site or all, and what changed recently. "Everything is slow" and "one application is slow for one office" have entirely different causes.

Then check the resource layers on the server:

• CPU — top or htop. High load average relative to core count, and whether one process dominates.
• Memory — free -h. The critical thing is swap usage; a server swapping is catastrophically slow, and this is often the real answer.
• Disk — iostat and df -h. High I/O wait, or a full filesystem. A full /var from unrotated logs is a classic.
• Network — netstat or ss for connection counts, and interface error counters.

For network problems specifically: ping for reachability and latency, traceroute or mtr to find where latency appears, and DNS resolution time — slow DNS presents exactly like a slow network and is a very common cause.

Note: Two points that impress. First, check monitoring history to see whether this is new or normal, rather than judging from a single snapshot. Second, always ask what changed — a recent deployment, a patch, or a configuration edit explains far more incidents than genuine capacity exhaustion.