I'm great at spelling (sorry, modesty wouldn't be helpful here) and would disagree with whoever said it's not a visual skill. It is very much so for me, aided by the fact I have a photographic memory - I can see any word once and pretty much spell it correctly thereon. Of my 3 dcs, only 1, my youngest, seems to take after me, sadly, on this. My elder two have been helped by learning common rules eg doubling consonants in verbs before -ed and - ing endings where the verb root has cvc or ccvc and the vowel is a 'short' one eg plan - canned/canning otherwise the e/ing would act like what I was taught at school to call the 'magic e', and will make the vowel a 'long' one eg ay not a. That's how you differentiate between canned and caned, or canning/caning, for example.
Sorry, not very well explained and I'm sure books cited above explain it better!
As well as the visual recall, I find that words in English do, in most cases, follow similar patterns. So if you can learn 'tongue', say, you can then handle other -ue words like vague without difficulty.
Knowing Latin also helps, as it enables you to understand that benefit is correct not benifit, as it derives from bene + fit (facere).
But I've not had to ever 'consciously' learn more than a handful of spellings, ever. Ones I do remember having to consciously learn include Wednesday, February, address, accommodation, separate and misled (well, the last one is pron not really spelling that I struggled with). Actually can't remember any others I struggled with apart from those ones!
I learnt to read largely by recognising whole words, once I'd mastered v basic phonics eg letter sounds and concept of magic e. Whilst this method is highly unfashionable now, I remain convinced that visual recognition of words is a far better way to learn to read if you value spelling skills as well. I don't know anyone who learnt to read by modern phonics methods who is a 'natural' speller. Whilst I can see that phonics is useful for eg dyslexics and those who would struggle with purely visual methods, I maintain that for most children, insistence on teaching reading through phonics is actually doing them a disservice.