Your people contact his people. Contracts are signed, deposits are paid. It's very unlikely that you would discuss the minutiae of a personal appearance with the personality themselves.
Be aware that the contract will generally come with riders, e.g accommodation, travel, meals, product tables, technical specs such as microphones, etc.; it's much more than a simple "Can you come and have dinner with us, perhaps say a few words".
Once you get something in writing, the personality WILL attend (barring serious events like illness etc). If they do not, the contract will have the penalties detailed in there, and word starts getting around that this person is not reliable. Reputation is everything in the after-dinner speaking world, so you can be sure that they'll do everything they can to make sure you're happy with their performance.