Study up on music theory
Anything and everything you know about music theory can and should be applied to any instruments you choose to pick up. Your knowledge of theory will likely allow you to pick up many concepts on your instrument that might take the average beginner years to understand or master.
Once you get a general idea of how your new instrument works, it should be a fairly simple process to use the knowledge you've learned on a different instrument to start figuring out basic scales, chords, or arpeggios on your new instrument. Once you're able to start grasping these, it shouldn't be too hard to start picking out songs or parts of songs that you've learned on your other instrument. Again, starting slow is essential, but your development on a new instrument will be drastically hastened if you've got a music theory background to fall back on.
You'll also find that going through this process will actually strengthen your grasp of theory as well. Since you have no (or limited) technical background on the instrument, you're relying on the theoretical knowledge you've developed. This will show you quickly where your knowledge is weak and will help you to strengthen said knowledge.
(Resources from the web)