The Shadow Trader is a tab of the Premium Shop. Each week he pays out one currency and takes every other one except Wraithgold, at rates computed from how long each takes to earn. What he pays in turns over on Monday 00:00 UTC.
1Open the tab
Open the PREMIUM SHOP from the menu and click the SHADOW TRADER tab at the top right of the counter.
2This week's target and the rates
The line at the top says what he pays in this week and what comes next week. Each row is one currency you can hand over, with its rate; drag a slider to choose how much, and ACQUIRING shows what you get back.
3Confirm the trade
Set your amounts and click CONFIRM. The server books the trade at the quoted rate - what you handed over is gone, and the target currency lands in your wallet at once.
Screenshots are taken from the live game by tools/tutorial_shots_b.py (dfmc-client) and regenerated after interface changes. The rules behind each screen: system-shadow-trader, system-premium-shop.