Ready golf is exactly what it sounds like: whoever is ready and safe to hit, hits. It's been endorsed by the USGA and R&A for years, and it's the single highest-leverage change a recreational group can make.
The rules of ready golf
Hit when you're ready, as long as it's safe. Walk straight to your ball instead of waiting at the cart. Put your bag or cart on the side of the green nearest the next tee. Mark and post scores at the next tee, not on the green you just finished.
Where it isn't appropriate
Tournament play with honors enforced, blind tee shots where you can't see the group ahead, and any situation where hitting out of order would be unsafe. Use judgment.
The compounding effect
Saving 30 seconds per shot doesn't sound like much. Multiply by 80 shots across a foursome and you've recovered nearly half an hour. That's the difference between a 4:15 round and a 3:45 round without anyone feeling rushed.