You should not need an opto, but you may want to include the series resistor shown in the .PDF Alain linked to.

A separate power supply for the servo is a good idea, but you need a common ground connection between the two power supplies.

Most hobby type servos will work fine with a DC supply of ~4.8 to 6Vdc. I normally use a set of 4 x D cells. Just connect the ground leg from your batteries to the ground leg of your regulated supply for the controller.

If you use another regulated supply for the servo, make sure it can handle the servo load current. A servo can draw quite a load. Some up to 1A or more. Having this load on your primary supply can drop voltage and cause a device reset. With separate supplies you shouldn't have this problem.