Peaches,
Speak to your employer about time off for governor duties. Some companies are quite good about this.
I'm a parent governor and work full time. Our meetings full governors and committees meet once per term. Different schools work in different ways, have a chat with your chair of governors to find out what would be expected from you. Are their meetings during school hours or in the evenings? (Mine are in the evenings).
I hadn't planned on getting hugely involved but 3 years in I'm Vice Chair of Governors, Chair of Finance and ICT Governor.
As Tommy said you can more or less choose how involved you get.