Before you start looking for an apartment, you need a preapproval letter.  Getting one is a cursory process that involves calling up a lender or mortgage broker, spending a few minutes on the phone answering questions about your income and financial history, and pretty much immediately receiving a letter stating that you are preapproved for a loan up to X amount at an interest rate of Y. 

It’s easy to get a preapproval letter. Too easy.

One of the problems of the letter is that not only has none of the information you provided been verified yet, but all too often, some critical nuance has been missed and inevitably surfaces later. Therefore, this piece of paper means very little beyond giving you a sense of whether you qualify.