Here's the thing.
If you want to trade items, you need to be at the trading post in a dojo. To get into a dojo, you either need to be in a clan or make your own clan and upgrade it.
In the in-game chat, you can see people would have posted their WTB/WTS listing. The chat goes too fast so it isn't visible. What you can do is visit the site mentioned below.
You can search for any item that you are looking to buy or sell, its price etc.
If you are looking for a beginner's guide, you can check out this person's channel.
As for anything else, you can visit,
The items that you can trade are mods, void relics, Weapons (Blueprints, Parts), Warframe (Blueprints, Parts), Warframe Helmets (Cosmetic) . For the rest, you have to buy plat to acquire the items.