Tools
Ping
What it does: sends ICMP echo requests and times the replies — the fastest "is it up and how far away?" check.
Setup: opens pre-filled with your machine's default gateway ("is my gateway up?" is the usual first check, and it answers even on an isolated/lab network with no internet uplink). Type any host/IP over it. Trace and Path ping default the same way.
Safe to run: yes, passive.
Reading results: replies with low, steady RTT = healthy. Timeouts/100% loss = the host is down, unreachable, or filtering ICMP. Some hosts (e.g. public IPv4 to 8.8.8.8 on some networks) are filtered even when the internet works — try a name or the IPv4/IPv6 toggle. A public host like google.com timing out while local IPs reply usually means the network has no internet uplink yet, not a broken ping.