As of Quasimorph V.0.6.2, the steps to trade hasn't been explained neither by the game nor any other guide, which has left a beginner like me confused as to how to do it. Luckily, after looking through a few other guides and videos, figuring out what exactly were people doing in order to trade, I've figured out the steps in order to do it.

I'll be sharing the steps in order to trade (or exchange) items with factions at their stations in Quasimorph with you here! Keep in mind that this can change as the game gets updated, so the method might change a bit. I sure hope that it doesn't change too much because I'm too lazy to update stuff like this but whatever.

1. Open up the stock exchange window on the main screen where you have your ship orbiting a planet and determine which faction you want to trade with. Here, check out the faction's "Rewards/Exchange" tab. This will give you an idea on what the faction will give you should you ever complete a mission for them or trade with them. I personally recommend either going with RealWare, AnCom, and/or SBN as they give you the most useful items like grenades and such.
2. Check the various stations that are owned by the faction of your choosing and the items that they accept for trading. You can do so by hovering over the stations' name (if there's no mission on said station) on the orbital map and looking at the item icons that appear there. The items that's shown in the station window shows the items you can trade there. Keep in mind that you can only trade said items on said station. They will not accept anything else to trade.
3. Travel to said station, picking a clone to take with you and stuffing the items you want to trade in their inventory. Note that once you're on the station, you can actually go back and forth between your shuttle and station cargo (the place where you trade stuff on the station), so if your character's inventory is small, you can still trade all the items you want.
4. Once you're down on the station, locate the station cargo by opening your map. It's going to be a yellow cross on your map. This is where we trade stuff. Go there.
5. Open up the station cargo and put your items there. Press the exchange button to trade your items. If your items are gone, the trade is successful! Depending on the amount you traded, you'll either get something or nothing at all. If you get nothing, well... Trade more if you want. The item you'll receive back will also be random but will be among the items you've previously checked out on step 1. If your items aren't gone, then the station isn't accepting those items. Make sure you've brought the right items!

And that's it! Those are the steps you'll need to go through in order to trade/exchange items with factions, gaining rewards (or not) in the process. I've found that it's quite a simple process, it's just that it's not properly explained to you on how to do it, making it seem like it's complicated.

I'm sure there's more to trading than just the steps above, but honestly I've yet to discover its intricacies so I can't really help you on giving you advice what to trade and how to farm the items. I still hope this guide is useful for you, especially for someone who just picked up the game.

Take care and have fun!