One of the main points of friction between me and the TF2 trading scene is that it appears you need to add random people as friends to do trading with them.
Is this true? How can I do Steam Trading with people that aren't in my friend list?
There are two ways you can initiate an out-of-game trade with Steam. You have to either be friends with them or be in the same group as them.
In both cases, the process is roughly the same. For someone you are not friends with but are in a group with, open the friends list, go to the groups tab and find the group you share.
If you are already friends with someone, you can simply use the friends tab.
Then, locate the person you want to trade with, click the triangle next to their name and click Invite to Trade.
Finally, you can now also start Steam trades merely by virtue of being connected to the same TF2 server. The old eight-slot in-game TF2 trading system has been retired, and thus the Objects → Trading → This server screen now invokes Steam Trading.
First you go to their steam community profile and select send a message:
As you can see the person is not my friend.
Then you can select invite to trade.
If you're specifically looking to trade TF2 items for TF2 items, you can do so through TF2, without adding someone to your friends list, you just need their steam community url. To do so, go into:
If you're looking to use Steam to trade (instead of going inside TF2) then you will need to add them as friends.