Study the form of each of the horses over the last 6 months over jumps, over distances, on good going and bad. Then cross reference that with the form for the jockeys. Then read every big race preview you can to see what the professionals think.
Finally after you've done all that, disregard everything you've learnt and just go for an Irish horse. Works for me most years.
I usually just pick by which one has the best name, although being an indecisive cow I change my mind about 10 times before the race. I'm working the day of the race this year so I'll put one bet on and be done with it (last year I think I put 5 on and basically ended up winning back what I'd spent).
The one thing I have learned to never ever do is bet on the favourite.
Alright, here's why. Firstly, it is a bloody long race with really, seriously big jumps; much bigger than horses usually see even on a point to point course. Second, there's 40 horses start running in it; way more than any normal race, so many that one interfering with another (no, not like that, the males have all been de-bollocked) can easily happen. Thirdly, the first fence is way too far from the start; that's why you get so many fallers there. Horses in a bunch, with people cheering them on run like hell and there's bugger all brakes on an out-of-control dobbin so most of 'em get to the first fence way, way too fast to jump it safely. Fourthly, the first few fences are hell on horses and quite a few get round the first time then see Fence One again for the second and think "Sod this for a game of soldiers" and stick the brakes on.
To choose somethings to back in the national, you want a horse that quite likes soft going (the course is mushy clay and a week's rain won't help), has won something recently or at least been out and not made a tit of its self, and hasn't been raced inside a month of the big race. Horses take that long to recover from a long hard race; racing knocks hell out of a horse. The Grand National is a handicap race, so the favourite will be carrying more weight (11stone 10 pounds, if I remember rightly) than any other horse; that's a hell of a weight to lug for a long race over big, big jumps. It doesn't much matter how big the nag is, as long as it can and demonstrably has run the distance in the past.
When betting on course, don't go to the first bookie you see. Look round; they all have to pay to stand and the best pitches cost more. Bookies are insured; they WILL always pay out, so go looking in the less-favoured pitches for better odds. Smart bookies (and I used to work for a smart one) know that sticking up odds of more than about 50-1 is a waste of time; you don't get more cash on donkeys like that, but you do get landed with bigger liabilities on 'em. So if you're betting on donkeys, bet each-way (check what the bookie is giving for each way; should be 1/4 of the odds, first four) and go roving about looking for a plonker of a bookie who hasn't learned not to put up daft odds. Deranged scotsmen are usually good for this sort of thing; if you see a certain Mr Moody there (Cedric to his mother), do give him my regards as he always stuck big odds on donkeys.
When you get your ticket, don't bloody lose it! Bookies work on the theme of "No ticket, no payment". Even if the horse loses, hang onto the ticket; there might be a Stewards Enquiry and the placings might get turned over, so don't be daft and chuck a ticket away.
Finally, if you're walking about on Aintree, keep your eyes down (people do drop cash quite a lot there) and keep your wallet very, very secure. The place is bloody swarming with pick-pockets!