since you're going over paint be sure and use an all purpose mud.
_using a heavy roller nap
_thin your mud 1 part water 3 parts usg green lid and roll out a 5 ft x 5 ft section onto your ceiling or wall.
_use a 10" drywall knife and pull that section back off into a pan(s)
_keep repeating until smooth........switch to a lighter weight mud in the process. If your mud starts getting dirty (grit) start throwing it out and using clean mud....very important.
there's also a floating method you could use that's not too hard to figure out.
after your first coat
_using a 10" drywall knife run your mud out in a straight line..a few inches out of the angle.....like you are bedding in a seam but not. cut your edges until your lap marks meet in the middle then pull smooth... treat your wall as if you had a series of seams every 12 inches. pull the full length of the wall ceiling...
let dry and then repeat the process but stepped over to where you are filling in the area between the last series.
after that coat
_roll out the entire surface again than pull the mud back off. Skimmed
hope this helps, I've seen some unforgiving knockdowns
this is mine