This really depends on the context and is much too vague to answer accurately in its present form. Are we talking about setting up a home network? Wireless or wired? How big's the network, are we talking thousands of computers or a couple?
If you're talking about a very simple home network then these days then I'd say there aren't really that many common problems - just make sure the relevant drivers are installed, you've followed the instructions given by whoever gave you your router and let DHCP do the work with all the address allocation and suchlike.
If on the other hand your situation is a lot more complex / specialised then there may be lots of potential pitfalls - but before identifying them you'll need to state exactly what it is you're trying to do