1) Go to the character tab. Go to the bottom, where it says 'make this character your main character' and do it (note you can only have one of these, so choose the right one).
2) Go to the equipment tab. On the bottom right corner of the box on the left, there should be a new icon that looks like a shop stall. That is the market. You can only see it if you complete step 1.
3) Once you're there, it's pretty self explanatory. Pick the dropdown on the left to select the item you want to offer, and the dropdowns on the right to pick the item and heirloom level you want to ask for. You can also specify an amount of gold. Be sure to format the gold amount like, "10000" not "10,000" or "10.000" as it will list either of the latter two as "10."
4) Hit "submit offer"
5) If you're looking for items, follow steps 1 and 2. Then simply look for trades in the list on the marketplace page.
6) Click "accept" next to the offer you wish to take.