Note: This guide applies to the Xbox Dashboard version 2.0.13599.0 (System Settings -> Console Settings -> System Info)
First, decide which IP you want to statically assign to your xbox. This should be a number outside of the range that your router will automatically issue DHCP addresses.
Next, in your Xbox UI, navigate to: My Xbox -> System Settings -> Network Settings -> (Either Wired or Wireless, depending on how your xbox is connected) -> Configure Network -> Basic Settings
Finally, you can configure your router to port forward the xbox live traffic to your statically IP'd xbox console. The ports to map are as follows:
When I initially configured my static IP for the xbox, I didn't specify a DNS server, since I had just assumed the router or the xbox itself would figure that out. However, after restarting the xbox, I noticed that it would no longer automatically sign in to xbox live. After some googling, I found mention of someone else running into a similar problem, and for them manually specifying a DNS server solved their problem. Once I manually specified a DNS server, my xbox has automatically logged into xbox live every time.