Find a company that occasionally lets people ride in their blimps. Goodyear takes the occasional passenger, but MetLife won't.
Learn what the company's criteria are for passengers. For example, if you are a sick child or know one who would like to ride in a blimp, contact Sanyo.
Contact local representatives of the company to see if it is possible for a customer to take a ride. Normally this happens if the company has a contest or raffle to benefit a local charity.
Suck up to local representatives of the company. See if they can get you on board the ship. This is the hardest way to swing a blimp ride; but it may be your only way.
See if you can get a job with a company that operates a blimp. Again, this is a difficult way to get a blimp ride; but there is always the slight possibility that you could swing it this way.