Bramley apple tree.

The key point is not to try and do all the pruning at once, it may take 3 years to get it productive by removing crossing/damaged/deseased branches in stages. 'The Fruit Expert' book has a good section on this. Make sure all the big cuts are painted with Arbex to prevent infections.

The other key point when prunign any tree is not to make it unbalanced, ie the centre of gravity vertically musnt be too far to one side, usually caused by lopping too many branches off one side.  If you  do theres a grave risk gravity and wind will bring it crashing down on the heavy side.

Motivator, you have been given some very good advice there from all three advisors.

Should you really paint any large cuts? We don't down here...

Yes, don't just give the tree a haircut! You need to be careful and selective about how you take wood out, although there will probably be loads of thin, straight-up whippy shoots coming off the main branches, they can go. You'll also need to remove crossing branches in the centre of the tree. What you want to end up with is something that looks a bit like a wide goblet. If the tree is badly neglected it will take a few years to achieve this. Winter is the right time to do this btw, so get cracking or leave it until next year.

Look on Youtube (search for apple tree pruning). There's a beardy bloke on there who gives very good demonstrations which we found more helpful than written descriptions or books. His videos showed me and Mrs Chuffy how to successfully rescue our neglected orchard trees. 

Good luck!