Dividing a plant up is an easy method of propagation.
Rhubarb is probably the best known plant using this method. It is advised to do this every five years to maintain the plant. I have yet to do this and they've been in the ground for 10 years!
Division is a good method for herbs especially container grown. Empty the container or dig up the plant from the ground and shake off as much soil as you can to see the root ball. Split the root ball, either tease apart or split with a spade and replant.
I have grown our chives from seed but once established it is so easy to use division to increase the plants. I have used the to create a border to one of the allotment beds. Another plant I grow at home in a container for ease of use.
Other herbs that work well using the division method are lemon balm, marjoram, mint and thyme.
Cuttings are another way to propagate herbs.