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The professional answer that you don't want to hear is sanding with a rotary (not random orbital sander) through grits 80 to at least 400 in four stages (i.e. 80, 150, 250, 400).
Then you have a surface very similar to the face of the board.
In fairness you can use thicker primers, filler etc if you have time and not the equipment to sand it effectively. If you are going in that direction I would use an MDF primer like Johnstones one which has a lot of solids in it and then fill with something like Toupret Wood Filler. It's not the best way time wise but you can get there with patience.
Airhead-
I have a little Makita palm sander which might be adequate? Having said that I think I'll try with some filler first, just in an attempt to avoid dust
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Applied some fine surface filler, sanded back and applied a first coat of primer (valspar stuff I had knocking about. It's got a reasonable amount of solids I think, but they drop out of suspension pretty quickly so you have to keep stirring.
Hopefully this will look ok after a light sand.
rhowe
Had a cupboard built from MDF. The carpenter left a few edges like this. I guess they need sanding back a little before painting, or do I use edging tape?