OH is in a similar position, new plot with old apple trees not pruned for many years. I'm no expert either, but my Grandmother has sage advice; cut out the dead and diseased wood, any crossing/rubbing branches first. If this is more than one third of the total tree, do nothing else this year. Clear the ground around the tree of weeds and grass and consider a compost/manure mulch to keep it weed free. I put cardboard around the base of my trees, water it and mulch over the top, works a treat.
Next look to prune for overall shape, if you overdo this you will get a lot of new growth ('water shoots' ; first year new growth which is thin and whip like) at the expense of any fruit so less is more, you can always prune a bit heavier in subsequent years when you tree has started growing more strongly. Aim to remove no more than one third of the tree at a time, old trees can be a bit shocked by drastic pruning. Look to keep the interior of the tree as open as possible (so a pigeon can fly through it!) so remove any badly placed branches.
Then the tricky bit: pruning to stimulate fruiting. Try and identify your tree if possible so you know if it is tip or spur bearing, can be difficult to tell at this time of year, but if it fruits see if the fruit is at the ends of branches, or on short stubby 'spurs' coming off the main branches. If you just cut the ends off the branches to make it smaller, if it is a tip bearing tree you will cut off all the bits where fruit is going to form! Try and cut the smaller branches and sideshoots back to the fatter 'fruit' buds: these will bear the flowers and fruit next year. It sounds bit complicated I know, but there are loads of online sites that can be more specific, hope this helps a bit!
