Not exotic equipment, that would be absolutely broken, but consumables, legendary equipment, ships, master work cores, legendary shards, sparrows, shaders, and even emotes should all be tradable.
To do it you would have to be inside the tower, in the bazaar and you would use the "storefront" emote and your character will spawn a little holographic table, you can them open your vault by pressing the emote again then you can select 3 items to sell for fun and profit.
In order to trade, you would have to walk up to someone's stall, click r3/rs and press options/menu and then select "Trade with player." As you walk up to the stall you will see a display pop up that shows you what items the player has for trade, and what rolls. After selecting "trade with player" a private voice channel is created between you and the shopkeeper. You can then begin to barter with each other. Simple and effective.
This would not ruin the game. Bungie said there would be trading in Destiny 1. There is no reason it can't be implemented. Some people have really bad luck with rolls and trading with other players would be an amazing alternative way to acquire some decent gear and get tube community to communicate and interact more. It would also improve the longevity of the game for some people because the kind of player that plays MMOs for the sake of being a virtual shopkeeper aren't being attended to.
I only bring this up because I was playing Warden of Nothing Nightfall with my clan and my clanmate and I got Warden's Law, and the clanmate who actually wanted it got NOTHING and he ran the nightfall like 30/40 times and still has not gotten the hand cannon. I wished I could have just given it to him but there was no option. I didn't even want it. It's just wasting away in my bank right now. Thanks Bungie, thanks Activision.