I want to confirm adding a switch to an existing stack.
1. Make sure all switches are on same IOS version
2. Adjust stackwise cables to include new switch.
3. Connect new switch and power up
configure ports and whatever on new switch.
The 3750s have a little more tolerance regarding IOS versions of stack members, and can do across-stack upgrades if need be. Cisco likes to say they'll do it automatically, but this is very hit or miss in our experience. However, we have been able to do IOS upgrades from one stack member to another that are running really incompatible versions.
All that being said, that series of steps seems fine. You'll want to keep in mind how you're connecting the stackwise cables if you're doing this live as so to not leave orphans.
Note that while you can connect stacking cables hot, Cisco recommends AGAINST doing so with the RPS cables (and in our experience the RPS 1300s are flakey enough to not tempt fate), so if you're using RPSes you're probably going to have to down the stack.