Settlers of Catan play takes hours
First, make sure you're following the rule that the person who's turn it is must be involved in all trades during that turn. If you let everyone trade during the trading phase, discussions could take a while.

Assuming you're following that rule, it really shouldn't take that person very long to figure out all of the available trades. If you start out by saying "I'm looking for sheep and ore. Is anyone willing to trade those to me?", you can very quickly get a sense of whether any trades will be possible. If anyone says "yes", you say "I have wood or brick that I'm willing to trade, are you interested in either of those?" Now you allow them to propose the precise details of the trade, or you let them say "I'm interested in brick" and you propose a precise trade. There really shouldn't be much of a back and forth; either there's a trade that both of you are interested in, or there isn't, and it shouldn't take more than a few seconds to figure that out. Yes, occasionally you will have a back-and-forth negotiation, but it shouldn't happen in the majority of trades.

It can take some practice to get into the habit of trading quickly and efficiently. I'd recommend trying out Bohnanza(bgg|wikipedia) with the group; it's a fairly quick and easy game that consists almost entirely of trading, so if you play it, you will get in the habit of trading quickly and efficiently or else the game will drag on forever.

Beyond that, it's really a matter of being disciplined while you play. In almost any game, if you allow people to take too long making up their minds or getting distracted by something trivial, it will take a while. Try and set a reasonable pace for the trading by example and by encouraging other players to trade efficiently, and it should speed up after a little while.