Supplies:
Messenger bag. I liked the look of this one and it was marked down at Burlington Coat Factory. Price: 20 bucks.
Foam padding. Closed-cell padding is better and thinner — you can find it at some fabric stores or camping supply retailers — but I went with some old packing foam I already had. Price: free.
Duct tape. Price: $3.95 because I splurged on a color roll.
That's it.

Total price: $23.95.

I picked the bag for comfort, a decent number of pockets, ease of access, and wide comfortable strap, but your mileage may certainly vary. Mainly, I didn't want something that looked like a camera bag ("Look! I have an expensive, easily pawnable camera inside!") and it had to have enough room inside for my stuff without being bulky.

First step was a sturdy-ish bottom. I used a sheet of foam from an old computer box, trimmed it to fit, and sliced two lines halfway through the foam where I wanted the corners to be. That way when I flipped it over and folded on those lines, I'd get a squared corner instead of a bent piece of foam.I could have just pieced some together, but I had a sheet large enough to keep it one piece.

This fits snugly into my bag, like so. I made it a touch wider than the bottom so it wouldn't slip around.

My bottom and sides.

Next I cut foam bits a little larger than I needed and wrapped them with duct tape. If I recall correctly, the foam packing once cradled a new hard drive.

Black or charcoal gray duct tape would probably have looked cooler, but I went with white to make it easier for me to find dropped filters, lens caps, etc. in the bag later. I made individual walls with the foam so I could easily piece them together with the tape, which peels right back off itself if I screw up and have to redo. And I did, a couple of times. Even wrapped in duct tape, it stays squishy and the tape helps keep your camera from catching on anything.

I crafted padding of various shapes to hold my camera face down, with a lens hood attached. Then I wrapped softer foam around it to form higher sides. No real reason to use different foam here, that was just the type I had in big enough sizes to wrap. I could have wrapped that foam individually in duct tape as well but wasn't sure how far my roll would go so I held off.

Here's the result. It ain't pretty, but my camera fits in it nicely.

And it fits quite snugly in my bag.

I pieced together some loose bits of foam into pockets for my accessories; filter adapter, filters, cleaning supplies, whatever. I didn't put a lot of work into that because I want to carry the bag around for a bit and see how I'll be using it. Duct-tape-wrapped foam walls can be easily separated from each other and retaped in new configurations, so no worries there.Here I just made a frame and stuck some loose, thin foam dividers in afterward.

The finished (so far), loaded camera bag. Camera secure, accessories stashed, camera already in shooting position as soon as I open my bag and pull it out. I can still access the interior pockets of the bag for more storage (batteries, lens cleaner, memory cards, pens, notebook, flashlight, Kruggerands, whatever you need). And the result is extremely light and I can move the compartments from side to side whenever I wish for more convenient accessibility. Doesn't look as snazzy but who cares?  The bag itself is comfortable to carry, soft against my hip, and sturdy enough that I won't panic about my camera gear.

It doesn't close tightly (this bag has magnetic catches) but I knew that when I bought the bag; just make sure you buy one you're happy with. The local Army-Navy store will likely have an incredible collection of just about any sort of carrying bag, pouch, map case or backpack you can imagine, and thrift stores can't be beat for the prices. Diaper bags make great camera bags, by the way; they're waterproof and that have tons of pockets.

And if I get tired of my bag or find one I like better, I can move my padding over or throw it out and do it again from scratch.

Total time: about an hour, mostly because I kept stopping and taking pictures.

If you like the customization but don't feel like mucking about with foam and tape, you can buy padded compartment inserts and mix and match as you like, but my way is cheaper.