I believe if you want to get acquainted with the speaker, you should take a few extra steps in approaching them properly. First, show up a few minutes earlier than when the event begins. Most of the time, speakers arrive 20-30 minutes ahead of time to get a feel for the room, the layout and make sure all their audio/visual needs are working properly.
Make an offer to distribute their handouts for them or be available to assist them during their presentation if they do not have a personal assistant with them. They will be extremely grateful and might actually highlight you and mention your efforts to the rest of the audience.
You can also offer to help collect their handouts or possibly provide them with help packing up. Taking a few extra steps to be helpful will definitely position you as someone they want to get to know better.
Most speakers struggle with marketing and promoting their speaking or consulting business. If you mention them to your co-workers or other people in your network, they will be eternally grateful. If you enjoyed their presentation, offer or send a brief testimonial for them to use freely on their website and other marketing material.
Make sure to get their contact info and follow up with them. If possible, schedule time to meet them to learn more about their area of expertise. Speakers are often extroverts and love talking about themselves!
What you might not know, is that most speakers have a huge following if they have been presenting for awhile. They can connect you to a variety of people and definitely worth getting to know better. Traditionally, they have a high profile and a very strong, credible, reputation.
Almost all speakers are authors or possibly send out a newsletter of some kind. If you start networking with them, they might actually feature you and your business in their publication.
If you know of some companies or organizations that book speakers, don't forget to make sure to offer them a referral!
Networking With the Speaker at an Event