Generally speaking.
First have a very sharp plane blade, from your post saying you've done some woodworking I assume you know how to sharpen tools... if not then that's your first step. Use a block plane such as a lie nelson 9 1/2, record, or stanley. Set the plane up so it takes off more than shavings but also isn't taking a bunch of material off.
I would strongly advise against using the sanding block you mentioned for a lot of reasons, you need a smaller plane or surface because if you use a larger plane or block you risk just flattening the board.
Something to consider before you take off any wood. Do you like the shape of the board? Do you feel it has the right amount of scoop and the right radius at the nut and bridge end? If so I would make a template for the radius of both ends. Then use a straight edge that is longer or at least the length go the board to see the scoop and make notes of the scoop at various points, different people have different ideas on scoop shape and depth but generally speaking the deepest the scoop will be is somewhere around the octave-ish.... if you are happy with all this then make notes of the scoop under each string and try to keep everything the same as if currently is, so all you re doing is taking off wood and ideally not changing the shape. The notes and templates will allow you to check your work along the way incase you start flattening the board. If you do not like the current shape that's a whole nother discussion on what to change and how to change it and there are a lot of varying opinions on the topic.
Second, I would just plane the whole length of the board in one motion from one end to the other, one pass at a time working from E to G or G to E, until you hit the whole board. Some boards like to go from nut to bridge some like to go the other way, depends on the grain you should be able to figure this out within the first couple passes. If after the first time over the whole board you can not tell where the plane is hitting mark diagonal lines on the board with pencil so you can see where the plane took off material.
Do this until the plane blade is making contact along the whole length of the board on every pass, again checking to make sure you are doing this in an even way across the radius of the board.
Depending on the thickness of the board, you may have a lot to work with or very little. So just go slow and check yourself a long the way. If you notice your are flattening the scoop just do a couple passes starting in the middle of the board and slowly make the length go the pass larger to not just dig a whole in a area. Plane until the ruts are gone. Use smaller straight edges to make sure there are not any peaks and valleys up and down the board.
After you are satisfied with the shape of the board I would use a small sanding block and sand from like 80, 100,150,220,320, 400, if you want 600. With wetting and letting the board dry to raise the grain twice with 150. Make sure you get all the tool marks out and that is a smooth radius, also be sure to slightly round off the edges of the board with 220 or higher grit. leave the board as is or finish it with.... wats danish oil, almond oil, again.... there are a lot of different thoughts on what to use for that.
Also since there are ruts chances are the nut will be too high when you are done, so you'll probably need to make the string slots in the nut deeper as well.
I am in no way saying this is the best way but it is a method, and since you seem pretty set on doing it yourself I feel this is a good place to start. The main thing is just make sure you keep the correct radius from E to G for the whole board and also be sure there is scoop in the board, but not too much.
