I have my grandfather's old model 62A and am looking to take it apart to clean it well. So far I've got the takedown screw twisted to separate the buttstock and front of the rifle. Where do I go from there?

That's about it.

After you've got the rifle separated, remove the upper tang screw from the top of the tang.
Bump the butt stock gently with the heel of your hand to loosen it, then slide it off the rear receiver.

Here's a good exploded view:
www.again.net/~steve/ipb-winchester-62a.html

As I recall, (it's been a long time since I was in one) the bolt can be slid to the rear and out of the receiver.

Using that diagram, how would I get the hammer out?

I wouldn't, but to remove it, you'll first have to remove the mainspring behind it.
That's parts 19, 20, and 21.
On some similar rifles, there's a small hole in the guide, part 19.  Cock the hammer, insert a pin through the hole to lock the spring, then remove the assembly as one unit.

To remove the hammer, once the spring unit is out, push out pin #15.

If there's no hole in the guide for a disassembly pin, be careful....this type of mainspring can be a BEAR to get back together.
Often these older guns were assembled at the factory with positioning jigs that held things in place.
Without the fixture, reassembly can be very difficult.

Thanks for the advice. I just stopped after separating the halves and cleaned what I could. Trying to preserve the old firearm for as long as possible. If nothing else, it made the action alot smoother.