Hi Eric Bee,
[quote]e.g., if I were to buy this bed frame:
austin.craigslist.org/fuo/4868448880.html
What the heck do I need to support the mattress?[/quote]
In a queen size or larger I would suggest a center support beam with at least two support legs to the floor first of all (four if the center beam isn’t attached to the headboard and footboard) something like this. Then you would need five 1x3 hardwood slats to support a suitable foundation or if you wanted to support the mattress directly on the bedframe without using a foundation you would need enough slats that the gaps between them were 5" or preferably less (for a polyfoam support core) or 3" or less (for a latex support core).
If you didn’t have a center support beam then I would use a support leg under at least 3 of the cross slats to support a foundation.
You could also use three steel cross supports like some of the ones that are linked in post #5 here.
If the side rails were higher (for aesthetics) you could also use a wire grid platform foundation like this inside the wooden bedframe instead of the center support and slats although I would be cautious with these for a mattress with a latex support core (see post #10 here).
Phoenix