That's actually an odd request .... because that is what stylists do ... connect with designers and pull for their clients. They have the contacts, they do all the work involved, keep the records, prep the chosen outfit, run around to get the samples and to get them back ... and they take the brunt of the negative responses, when designers don't want to lend. You might get your feelings hurt and you will have to do a lot of physical labor to get it all done in the time they allot.
But ... if you want to try ... here's the drill:
Contact their publicity/PR people in advance and ask to make arrangements with them. You will have to find a way to convince them you are who you say you are and must prove that you are attending a very public event where you will be photographed by the press. The only reason they lend is to get mention in the press ... so that needs to be your focus when you talk to them.
First, they will decide if you are press worthy enough.if your look suits their image and if they are interested in being shown at your event. If you are a major star, you will have pick of pretty much anything you want ... they will even call in samples that are out to other stylists, if you are "big" enough. However, if you are a lesser known person or the event is not of great interest to them, they may limit it to a few selections from a previous year or may just say no.
If they do lend some samples, usually they will not release them until right before the event and need you to return them the day after the event ... 24 hours is all you usually will have to get them all back. They will need them for someone else to try on. So you have to be prepared to schlep around a lot ... right before your event and immediately after. Plus, if you are not in the city where their samples are, they will ship them to you, so you will also have to steam and prep them yourself the day of the event. Then, of course, you must pack it all up and ship it back, ASAP.
I would think you'd need this time to prepare yourself ... spa, hair, makeup, etc. So it makes me wonder why you think that you have the time and energy to do all of this yourself. Your stylist is a very important part of your team .... and offers a valuable service and has the time and the knowledge to be able to get this done efficiently.