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If they are just simply clear liquid then you could sterilize a needle by boiling it in water or holding it over a flame for at least 30 seconds then poke a hole into the cyst and gentle squeeze it to release the fluid. However if the material in the cyst is thick or sebaceous material like from a sebaceous cyst then it is unlikely you will be able to get the material out from home.
One thing about cysts is that they will return and many people opt to do nothing with them because of this and the fact that they are rarely a bother to the dog. You do increase the risk of infection which could become serious by draining a cyst from home just so that you are aware of that.