Microsoft has just released a nice video on optimizing network connectivity for Office 365:
A lot of connectivity to Office 365 is not in your control. However, you should have an understanding of connectivity to the data center to your tenant. In some cases, MS has worked with ISPs to optimize connectivity in cases where there was obviously bad routing. For example traffic being routed unnecessarily over trans-oceanic links.
If you have high latency to Office 365 you can use tools such as PSping to look at connectivity. PSping performs a connection to a service at a port number rather than using ICMP packets as regular ping does. You can also use Network Monitor to identify some issues.
PSping is free from Sysinternals: