Trade in Path of Exile 2

You can trade almost everything in Path of Exile 2. Whether it's the gear you pick up off the ground, crafting currencies you use to make it, or the rewards from killing a boss there are plenty of opportunities to buy what you need or sell your unwanted items.
However, one notable exception is gold, this is used to purchase items from vendors, list currencies on the exchange, and respecialize your passives. You gain gold by killing monsters and it CANNOT be traded to other players!

Poe2 Exchange
The Currency Exchange is an asynchronous trading system where you can list various currency items. If this works like PoE1 you can list anything that stacks. This may include;
Basic currencies like Chaos Orbs or Exalted Orbs.
Runes and Soul Cores
Atlas mechanic rewards like Essences.
Crafting currencies from endgame activities like Omens and Catalysts
Uncrafted Waystones and Tablets

You cannot list gear, or items that do not stack such as:
Unique items
Crafted Waystones and Tablets
Crafted Rares
Jewels

PoE1 Exchange Mechanics
You begin by selecting the currency you want, and the currency you have. In this case, the currency you want appears on the left side, and the currency you are selling appears on the right.
The Currency Exchange Market supports all stackable currency items. Based on what Jonathan said previously, the PoE 2 exchange should support all of this plus regular items as well. You can use the search box at the bottom to find a currency more quickly or use the tabs on the left for quick navigation.
After selecting both currencies you need to set a ratio. Common market ratios are shown for your convenience. After you set the ratio you can place your order and pay the Gold fee. The amount of Gold required scales with the number of currency items being traded.
Once there is a purchase request for the same currency with the correct ratio, your order fills. If there's no compatible open order you may need to wait a bit for the order to complete.

Direct Trading
Almost everything in Path of Exile 2 can be traded with other players. This includes the items listable on the currency exchange market. If you're looking to trade uniques and other equipment, you need to use Path of Exile 2's direct player to player trading systems. You need to invite someone to your party, then travel to their hideout (or wait for them to travel to yours) to trade with them directly. Open the trade window, and select the items you wish to sell. Then, double check the contents to ensure you're getting what you want then click accept.
Now, one way in which Path of Exile 2 differs from many other games, there isn't a universal trading currency. Remember, Gold is untradable so you're not going to be selling things for Gold. Instead, Path of Exile 2 uses a barter system, where players agree to use different consumable crafting currencies. In Path of Exile 1, players commonly use Chaos Orbs for smaller trades and Divine Orbs for larger ones. We don't know what currencies players will use for Path of Exile 2 but Chaos Orbs and Exalted Orbs are both definitely a possibility!
If you want to list something for sale, you can place it in a public stash tab and then set a price. After you change zones the item should become visible to all players via the trading website, you can go back to exploring the atlas while you wait for a buyer to message you.

Trading Websites
But how do you know what someone has for sale? If things work exactly like PoE1, this is where a trade indexer comes in. You can do this via the official Path of Exile Trade website maintained by Grinding Gear Games. Trade Indexers provide a variety of options to filter public listings for your desired upgrade. You can search by base type, implicit properties, affixes, and much more! After that, copy the trade message to automatically contact the seller and begin the buying process.

Summary
Almost everything in Path of Exile 2 is tradable. The game has an asynchronous trading system in the Currency Exchange Market where you can use your Gold to list bulk currencies. You can also trade your gear directly with other players. Unfortunately, the details are few and far between, but we look forward to learning more as the early access unfolds.