What are some strategies for winning a lease for an apartment when there are multiple people interested?

You want to show up with as much information about you and your roommates as possible - and references to your responsibility and reliability. If you can prove to your potential landlord quickly and easily that you will take care of the property and will make his/her life easier, you'll be in a great position. Bring as many of your potential roommates with you as possible, so the landlord can get a sense for who you are as people.