After you submit your application, you'll wait to hear back. Depending on the landlord, you may hear back in two days or two weeks. If you applied through a property management company, you'll probably hear back sooner because they have dedicated staff for reviewing applicants. If you applied to an independent landlord, you'll probably be waiting longer.
If you haven't heard back after three days, you should send a polite follow-up email like:
This is John Smith. We just want to follow up on the status of our application with you for 123 California.
In the meantime, you need to keep applying to places. If the landlord takes two weeks to tell you, "You didn't get the place, sorry!" then you'll be two weeks behind. And if you get two weeks behind, you're going to be more stressed out. We don't want that to happen to you, so after you apply to one place, keep looking until you hear back.
When you do hear back from one of the landlords and move onto signing the lease, we suggest sending the other landlords a note along these lines:
Thank you so much for considering us for 123 California Blvd. We just heard from another landlord for a property we applied to, and we're signing the lease this week. Just want to let you know so you don't spend unnecessary time evaluating our applications.
This isn't necessary of course, but it's a good idea. This way if your current option falls through (for whatever reason), you may be able to reconnect with one of the other properties you applied to. Who knows, maybe they have more than one house.
Keep Applying: You're going to need to keep looking for places. It's not over until you sign the lease!
Keep Other Landlords Updated: When you hear back, let the other outstanding landlords know. They'll appreciate it.