I think I have good form with a straight, neutral back on my squats and deadlifts, but I don't know that I am keeping my core "tight".  I cannot suck in my (considerable) gut, but instead find myself pushing out.

Assuming I am not rounding my back, is this OK?

http://startingstrength.com/video/lifts/the_squat_starting_strength_dvd

Take video to check form.  You'll learn a lot fast.

A belt gives you something to push against, some people think that they have a tight core because they are pushing their belly out, but your core is more than just the belly.  You'll feel dumb practicing it so don't do it in front of your wife, but wear a belt and practice pushing out against it with your entire circumference.  You'll feel the sides and back pushing on the belt when you do it right.  And when it's right you're a lot stronger.

This also dovetails into breathing right.  Your breath will help fill the core with air and make it easy to be solid.  Lots of good videos on this, look for Duffin's video.

Like SCW said, look for anything about Christ Duffin talking about bracing. It is basically the same action as tensing up like you are going to get punched in the stomach.

If I was expecting a gut punch I'd brace tightening the muscles and pushing them out.  Sitting at my desk the whole action almost feels like trying to grunt out a turd.

As as for breathing I find that almost impossible to do while pulling the abs in.

Quick trip down wikipedia and maybe I'm using my diaphragm to stabilize my trunk instead of my abs???

I will try taking video of the exercises -- I have loathed to in the past because I didn't want to look like an IG tool, but absent an actual coach this will probably be my best bet.

And on Part 4, Rippetoe tells a lifter "get your abs in", which I find conducive to neither stability nor breathing.

or

I told you that you'd look stupid, lol

I actually 'learned' a lot of this one day in a crowded gym- I squatted down and let out the biggest, longest and full-breath fart in my long career of letting out nice farts.  The next rep I clamped that valve down with everything I had and my squats were the easiest I'd ever felt!  Ahhh, that how to turn on glutes!  

If you wear a belt you can practice until you feel yourself pushing out against the belt in 'all' directions, not just the belly.  It takes a while to learn how to turn on muscles in the sides and back but with the belt you'll get that feedback and you'll be better at it pretty fast.  Breathe deep into the belly, let part out, breathe deep again... like filling up a bit at a time.  For a big lift you're really tight and hard and ready to hold a lot of weight.

I use a stomach vacuum move to practice. Basically letting air out with the diaphragm, while trying to suck your belly button towards your spine. Then hold that position while breathing.

It's not the same as setting up for a deadlift, but it helps me with the connection required to engage everything before pulling.

Lots of good info here, but I remember this being hard to truly understand so I would start simple and then work up. The simplest way to put it would be to suck your ribs slightly down towards your hips while squeezing your glutes. If you did this while planking and looked to the side at a mirror your back would be pretty damn neutral right? If somebody gave you alight punch to the gut you wouldn't feel it at all, right? That's where you want to be.

Duffin  has another video where he explains bracing to Mark Bell on his Super Training YouTube channel.  Watch it.  It's is the correct method.  

The weight belt is there for your abdomen to push out against.  It's like the cables on a suspension bridge.  You can't lift heavy weights safely without proper bracing.