I use hamachi to play with my friends, and sometimes it takes a little messing with to get it to work.
Step 1 - Start Starbound Server
Step 2 - Create a new network in Hamachi (if you have a old network, delete it and make a new one. I do this every time)
Step 3 - Select Multiplayer and enter in your IP address
If you get into the game, your server is working, if you can't get into the game try restarting the server, create a new network, or do both.
Step 4 - After you're in your server have your friend join your Hamachi network
Step 5 - Have your friend select multiplayer and type in your server IP
Again, if this doesn't work try restarting the server or network. Most of my issues came from having my friend in the Hamachi network before I got into my server. So try getting into your server then have your friend join the hamachi network.
Also, a couple of times a simple restart fixed all issues.