Apparently there is some background information that is needed for this thread or the answer is relatively easy. Just use three cameras at the same time, capture into Vegas sync up the 3 tapes and edit to your liking.
Are you wanting to do live showing while the preaching is going on? What are you trying to accomplish by using 3 cameras?
Do a search on "multicam" and you'll find dozens and dozens of posts. jrazz is exactly correct on how to do it, but there are all sorts of tricks that can make syncing the cameras on the Vegas timeline much easier. Also, there are several commercial Vegas script products that can make editing multicam projects very simple. Check at both the VASST and the jetdv sites.
Now the church leaders are wanting to know how we can record from 3 different cameras at one time.
You might want to take a look at Scenalyzer Live. It can detect multiple cameras connected via firewire and capture them at the same time. You need to do testing and may also need multiple firewire cards.
Alternately, you could do a live mix and then just capture the mixed version live.
As you'll see, he is also involved in church work, and he also has lots of hints on using Vegas, along with a place where users post their Vegas works.