Apartment lease agreements usually aren't terribly complicated, but if you see a home that you love while looking for a rental apartment in New York City, you should be ready to apply on the spot. The apartment's landlord or management company will supply the application itself—it's a fairly simple form, and shouldn't take more than a few minutes to fill out—but you should have copies of all the necessary back-up documentation at the ready, including:

• A signed letter of employment, on official company letterhead, stating your current position, annual salary (guaranteed plus bonus, if applicable), and length of employment. Your company's Human Resources department can usually help you with this. 

• Three most recent pay stubs.

• Your most recent federal tax returns, especially if are self-employed, and can't provide either of the above. (Note: not all management companies will ask for this, but it's good to have on hand, just in case.)

• Up-to-date copies of your bank statements, both checking and savings accounts.

• A letter of recommendation or verification from your current and / or previous landlords.

• A list of references—your accountant, or lawyer, or past employers—with phone numbers, to put on the application, if necessary.

• Your check book.

• A photo ID, such as a driver's license or passport.
   

Once you're done with the rental lease agreement application, and have handed over all of your paperwork, the landlord or management company will run a credit report on you (at your expense), and let you know if you've been approved, usually within a few days.

A good rule at this stage is not to get too excited about a apartment until you have actually signed the lease. Remember: there are likely other applicants for the same space, so better to keep your expectations in line to avoid the heartbreak of "losing" a place you never actually had.