You should take MTR Tung Chung Line from Tung Chung to Hong Kong Station at Exit F and then go to ferry pier no.5 to take ferry to Cheung Chau.
Here is some details for Cheung Chau ferry service schedule:
http://www.td.gov.hk/transport_in_hong_kong/public_transport/ferries/service_details/index_tc.htm#o01
Fee:$18+($11.5/$18/$22.5)=$29.5 up(For Monday to Saturday)
$18+($16.8/$26.2/$32.2)=$34.8 up(For Sunday and public holiday)
Time:45 mins+55mins-1 hours(for thr ordinary ferry)/35-40mins(for the fast ferry)=1.25 hours up
Also,you can take the bus no.3M to Mui Wo and change the Inter Ialands to Cheung Chau,bus the schedule for Inter Island services frequenty is very low so I suggest you to take MTR to Central and then change ferry to Cheung Chau.
Fee:$10.5/$16.2+$11.1=$21.6
Times:31-35 mins(From Mui Wo to Cheung Chau journey)+1 hours=1.5 hours
Here is the Inter Islands service schedule:
http://www.td.gov.hk/transport_in_hong_kong/public_transport/ferries/service_details/index_tc.htm#o01
Cheung Chau to Central ferry service schedule is over-night.But the night schedule frequenty is very low.For the last ferry to Central,it is departmental at 11:30pm(for Sunday and Public holiday).It is ordinary ferry.For Monday to Saturday,it is departmental at 11:45pm.It is fast ferry.If you want to take ordinary ferry,you should take the ferry departmental at 11:30pm.
Hope above information can help you!