For the benefit of newcomers to the AM3352-SOM with the Olimex V3 image:
After you get a network interface to work (remember that VLAN is on for the built-in switch - use a USB adapter for starters), you will probably run into the package manager reporting errors.
The repair is to fetch the missing keyfile for one of the repositories manually, and install it:
First, fetch the deb package to a file in home:
(Update the file name if the version changes, e.g. by using a browser to find the file first)
Then, manually install the package:
sudo dpkg -i rcn-ee-archive-keyring_2015.06.08~bpo90+20150608+1_all.deb
Voila, now apt-get works correctly.
sudo apt-get update
sudo apt-get upgrade (optional)
sudo apt-get install whatever-package-you-needed