I am pretty good with numbers and maths etc, so am hoping to get to grips with this as best as possible.
You can either treat it as a recipe - do what it says in the book and believe the answer - or you can try to understand what's going on, which personally I prefer as I think it'll be easier for me to spot gross errors if I understand the process. All the whizz wheel does is solve vector triangles - to understand how it does this is just a matter of drawing pictures and thinking about it.
Point is, the whizz wheel is supposed to be quicker and easier than either doing the trigonometric calculations with algebra or drawing scale vector triangles on a piece of paper and measuring them; you can use whichever you like for pre-flight planning; in the air, if you have to re-plan a diversion because of weather or something, like I did last Saturday, it's estimating and mental arithmetic (by any of the means discussed here from time to time) and rule-of-thumb (the rule being that a thumb is six miles wide on a half mil chart).