It can be a good thing or a bad thing when that notice comes through that a tenant is moving. If they were terrible, called at all hours, complained about everything, all while never paying their rent on time, you're probably happy to see them go. What you're likely not as happy about is the fact that it's now time to get the property ready for a new renter and find
that new renter.
Hopefully you were able to do a walk through with the out-going tenant before they were gone entirely. This will give you a chance to go over any cleaning that they might have missed and help them to get more of their deposit back. It's really a win-win situation. You have to do less to prepare for the next tenant and they receive their deposit. Assuming that they didn't leave utter destruction in their path and you weren't planning any major upgrades to the property in between, this should be a fairly quick process.
Next comes the part that many landlords hate: marketing your rental property. We do live in an age with a wide variety of possibilities at our fingertips. Free sites allow you to post your property, photos, and descriptions online for thousands of interested renters. Make sure to post to multiple sites to reach as many people as possible. Yes, this will require more work out of you when you receive tons of applications and you start the screening process, but it'll also help you find the best tenant possible. Finding those fantastic tenants is always the goal.
Make sure that you give the potential-applicants a good feel for the property. Fill out as much as you can on the online templates, provide clear photos and descriptions to them if it's allowed. The better idea a person has about the property before they actually step foot onto it, the more interested they'll be.
Check out these tips from BiggerPockets on writing awesome property adds
to get a good idea for what is needed to really catch the attention your property deserves.