When I'm offered a position, I always ask for them to review the contract template I've written and to either fill in the blanks, or use it as a guide and send me an e-mail/document so we can all be on the same page before I officially accept the position. I usually hear from them within 24 hours (though I would say 2-3 days is acceptable depending on the start date).
If I haven't heard from them by day 2 or 3, I'll give them a call and see what's up.