What is the best way to remove rawl plugs?

I've got the little beggars out of bare brickwork by inserting a woodscrew part-way only, then using a claw hammer under the head of the woodscrew. If you try this, put a wooden pad against the wall, to spread the pressure from the hammer head. In your case, it would be very easy to break out a crater of plaster as the plug comes out, so it might be safer to use filler over them. If they are a bit proud of the plaster, try knocking them in gently: hold something like an inverted woodscrew over them, and tap that with your hammer

Of course, if you actually tried hanging shelves on them, they would probably pop out like champagne corks!

Alan E is correct but I fit the screw part way in then I use a pair of pliers and a scrap of wood to gently lever the dowel, raw plug or any other plastic plug. By the way there is a special fixing for plaster board. It is like a large screw which is screwed into the plaster board then a second smaller screw supplied with the fixing is screwed into the center. I suggest this fixing for permanent things like shelves or wall mounted cupboards, and heavier items.

Do not remove if they will not pull out easily, those that stick can be cut off flush to the suface, next get a countersink bit on your electric drill and countersink a fairly wide shallow hole in the surface. This hole can be filled with polyfilla and made smooth, the filler will stick to the wall material at the base of the depression and will not fall out. I have repaired similar damage to yours and this works every time, it's not much more work as you would have to fill the holes anyway and you will get a much better finish filling the enlarged holes.

you can either nock them further into the wall saving in filler, use a screwdrriver to do it with.

or thread a screw in to the plug a short way and then pull the plug out with pliers.

if they are plaster broard fixings ( silver circle with what looks like a plus in) simply unscrew with a scwerdriver good luck

i find the best way if they cant be pushed in anymore and filled then screw a screw in just enough to grip the raw plug and then use plyers to pull the screw out and the raw plug comes with it