Hi Jacquie - I don't grow Schlumbergeras, but hand pollinating flowers is easy! Here is a basic explanation using @dirtdorphins
utterly awesome close up of the reproductive parts of a Christmas cactus.
The Male parts of the plants are the Stamen and Anthers. The Anthers are on the tip of the Stamen and hold the pollen then release it when it's ready. The Female part is the Pistil. That's where the pollen wants to go.
In the picture on the left you can see one of the Anthers just starting to release the pollen. On the right the Anthers already have released it. The Pistil is where the pollen needs to go. To collect the pollen you can use cotton swabs, a fine tipped paint brush or pull off one of the stamens with the pollen on the anthers, (won't hurt the plant at all). With your tool of choice, brush the pollen with it and transfer the pollen to your tool. Then gently brush the Pistil so the pollen is transferred to the Pistil.
That's all there is to it!
You'll know if it 'took' if the base of the flower starts to swell in a few days or weeks.