Trading is finally live in Pokémon GO, but it isn't so easy as finding someone with a creature you want and filling out your Pokédex. No, developer Niantic Labs has instituted a sort of transaction tax to keep the new system from distorting the in-game economy or encouraging shady back-alley meetups. Trading costs Stardust, still one of the most valuable resources is in the game and not easy to part with, particularly in these quantities. Different Pokémon take different amounts of Stardust to trade, however, and the amount of Stardust it takes goes down depending on how good friends you are with the person you're trading with.
Luckily, we have the Silph Road to collate all the data is this relatively complicated game and put it all in one place for whenever we need to refer to it. So here are all the Stardust costs by friend level, with credit Janka_lml for putting it together.
As you can see, the prices get pretty steep if you're trying to fill in your Pokédex with high-value creatures by trading with people you've just met. The most expensive trade on this list is for a Legendary or Shiny that you don't yet have in your Pokédex, and it will cost you a whopping 1,000,000 Stardust. Getting to be better friends will help immensely with this, however, bringing the cost of the same trade to a still-substantial but eminently-manageable 40,000 Stardust.
You can level up your friendships by sending gifts back and forth as well as battling in Raids together. If you're sending gifts, it should take 90 days of continuous gift-giving to rank up to the coveted "Best Friend: level, at which you can really start to take advantage of your expanded social network.
Right now, it seems like the easiest way to use this system to round out your Pokédex sooner rather than later would be to snag some Regionals, which only cost 20,000 at the good friends level. That will also, I suspect, be the biggest safety issue for the game going forward. Regionals are highly desirable, and the ability to trade with an essential stranger could lead to problems. But trading only requires you to be within 100 meters, so stay safe and don't give any identifying details about yourself to someone who you want to meet to trade, or better yet don't trade withs strangers. And when you do, never exchange money, only Pokémon.