What you can do depends on your network topology and your specific OS. Someday, I hope, people will include a few details with their questions. But I will assume that your network is identical to mine and work from there.

Every unix system that I know of has some way to see statistics kept by the lan driver. With HP-UX, lanadmin can do that (in menu mode). At best, this will only enable measurements on the local ethernet segment. And these days, even that becoming very rare. Your average unix host is connected to an ethernet switch and can only see packets to and from it. Still, this is a start and you should ensure good communications with your system's link partner.

To measure latency across a complex network, traceroute is an option. If your routers and firewalls allow traceroute to work, it can tell you where a delay is...if it is a persistent delay.

To measure performance host to host, I usually just ftp a 1 GB file and time the result. I know it's low tech, but I like that. Most ftp clients perform the timing automatically.

Routers and switches keep on-board statistics. They tend to have a service port that you can access via telnet. They can also report their statistics via snmp but this requires software that you need to purchase. Your network team should be using these or some other technique to monitor their boxes. I am not an expert in this stuff so I cannot really comment further. But if you are your "network team", you need to check the docs for your network boxes to see what is available.