Sign in with Steam
This allows you to authenticate yourself without requiring to enter your Steam username or password - it's fast and safe.
Pick a trade
Then add the trader to your friend list on Steam, invite him/her to trade and just do it.
Make an offer
After clicking on "Add items to offer", you have the option to make an offer by selecting items from your backpack. You can also send a message by entering some text in the text area. This it is optional as well but you must either select items, enter text or do both.
Read trade notes
If someone specifies rules of his or her trade, please do respect them. Don't add a someone who doesn't want it, just post your offer and wait for a response.
Make your own trade
Use "add trade", to prepare your trade. Pick items from your backpack as [H] and select some from list of all items as [W]. If you want, you can enter an optional message that will be displayed under the trade, and click Post Trade to finish.
Add "+ More" to your trade if you're out of slots. E.g. If you want to trade few sets of items and/or you are willing to give more than you could put in other 7 slots for single very expensive item (worth more than 8 slots can handle). Do not create trades to bring attention. E.g. Timebreaker for Dragonclaw Hook. Put most valuable items in first 7 slots and add "+ More" as last one. I warned you.
Control your trades
In "my trades" you'll find all of your active trades. You can bump them every 30 minutes to show them as first on the "main page". If someone makes an offer, you will get a notification next to the trade. You can disable single items that you have already traded. To close one of your trades use the "Mark as done" button.
In my trades just next to your trades, you'll find a list of all matched trades that contains the same items you wish to trade. Check those trades, contact people, and trade.
Search for items
Search allows you to find the exact trades that you're looking for. Pick items from your backpack and/or from list of all items and then click "Search". It is possible to fill only one side of trade to search. You can move items from the right side of the search to the left in order to check its pricing.
My offers gives you insight on all active trades that you placed an offer.