If you have a pattern where you tend to fly a particular airline most frequently, its program might be a good place to start. If you sign up for a frequent flyer program, say, with United, Continental, or Us Air, you'll generally be able to redeem your miles on other star alliance member airlines. Some are more generous than others with allowing awards on partner airlines, e.g. there was a time when United was blocking most Lufthansa awards. To get the best bang for your buck, you'll want to research the stickies and key threads in the particular airline's forum.

If you don't already hold credit cards that earn miles in a program, that's an excellent way to rack up lots of miles quickly. Research the "special credit cards offers thread" and do exactly what the first and last posts recommend. E.g. there was a time when you could get 75Kx3 AAdvantage miles if you applied in just the right sequence. These offers do change frequently.

I haven't heard of airlines allowing businesses to sign up for frequent flyer programs. In any event most will allow you to book award travel for individuals other than whose name is on the account but the earned miles generally accummulate into individual accounts and usually cannot be combined without paying high transfer costs. British airways might be unique in that it has "household" accounts where miles can essentially be pooled. Works great for AA flights but is very costly on other partners due to fuel/whatever charges.