Curtains don't get walked on so any surface dirt is usually airborne dust. Most of this can be removed by thorough vacuuming. They can then be either towel cleaned by spraying either an encapsulator, microsplitter or colloidal detergent onto the curtain then towel off with either terry towel or sponge.
A plasterer's hawk (plastic) is a usefull accessory as you can hold it behind the fabric to give you something to push against.
It is important to really check them before you start as often the fabric is severely degraded due to either sunlight or air currents moving continously through the fibres. You also often get water marks if they are lying on the window sill. Of cause you can also extraction clean them after testing for shrinkage but what a ball ache that is, however a proper curtain tool does make it a lot easier.