Steam allows you to send a trade to any user even without adding this user to your friend list and even if this user is currently offline.
These things are called "Trade Offers". You can read about the "Trade Offers" here. The following instructions describe the process of trade creation.
Step 1.

If the user you want to send a trade is your friend, then open your inventory page, click the "Trade offers" button and click the "New Trade Offer..." button.

If the user you want to send a trade isn't in your friends list, you need to find his Trade Offer url. This url can be found on forum boards or items trade websites. For example, you can find the Trade Offer url in comments on Steamprofit. You need to go to this link.

Step 2.
In the trade window select the "Your inventory" tab, then select an application and choose items you want to trade. After that select the "Their inventory" tab, and choose items you want to get in trade.

Step 3.
Add a comment to the trade for information purposes.

Step 4.
Confirm the trade by checking the "Click here to confirm trade contents" checkbox.

Step 5.
Check everything one more time and press the  "Make offer" button.

Step 6.
Confirm your trade via email (more information about email confirmation here). Information about how to disable the email confirmation is here.