Exchange other resources for gold?

You can. In the diplomacy screen, hit trade. On the left, select a resource and then however much. Click on OK. The worth will be shown in the trade box for how much the AI is willing to trade for that. You can trade multiple resources at once.

technically you can. but in reality no, you cant.  never saw an AI that would give squat for materials or more than 1gp each for crystals and horses.  i did get a fair price for metal once but thats it (the other AIs all had enough metal that they wouldnt give me anything)

real trade at set rates would be an excellent improvement to minor factions.

That's odd; I've very occasionally gotten 11 gold per crystal; 7 is pretty common for metal or crystal.  1 or 2 is common for diplomatic capital, and materials are usually considered pretty worthless in trade.  As sagittary suggested, I think the original poster just didn't click 'OK', to accept putting the materials on the trading 'table'.  It's always irritating when I forget that (not very intuitive, I'm afraid).

EDIT: You're right about horses - for something so rare and valuable, it's odd that they're always valued at 1 gold / horse.  Makes it easy to trade for them when another faction has them, though (exploitive, really).

I'm used to computer selling crystal for 200 per...so it can really depend...

Does it have to be with the AI? What I meant by the question was can you trade them "with yourself" like in a market or such?

 @BryanKMills - no

just double checked my values.  best i could do was 7gp per crystal with an AI that had zero crystals and a relationship of "Close".  if they have more than 100, the value is zero for every resource.

other modifiers?  map size? difficulty? AI tech levels? 

like i said: minor factions need to be used for something... why not trade centers?

So you want to create a trading post where you can trade for items at a set price rather than with other kingdoms?  that might cause a lot of problems with the trade economy of the game as why would any one ever want to trade with another kingdom and use diplomacy?   but i agree that most of the time the trade options in the games i have played are either way too expensive or simply not needed. 

The AI never wants any of my stuff. I would rather have my own market to trade unneeded resources for gold or items I do need. There can be different prices for buying and selling to keep balance. In one game I had 6K in material, why not allow me to sell 10 material for 1 gold or something like that.

I never use this option. The game is very easy, so neglecting it gives a bit more difficulty.

I know, this isn't a real solution.

Waiting for better AI. Fighting, building, traiding . . .