How to analyze this Diode Circuit by hand?
"Analyze" is really quite general. What are you specifically looking for? Usually, with diode circuits you start with a guess: is the diode conducting or not? Let's guess that it is.

If the diode is conducting, in a simple circuit such as this, you can replace it with a .6V (or whatever your diode drop is) voltage source and proceed with nodal or loop circuit techniques. After you've done this "analysis" using whatever technique, check against your initial guess: is the diode indeed conducting? If not, start over with the assumption that it is not conducting.