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.
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.