If you want to challenge or oppose a friend's trade (one you think will go the other way), you can do so from anywhere you see a trade ticket.
The most common places to see a trade ticket is on your Activity Feed and within any Groups you're a member of.
To see trades on your feed, you must be following someone.
To inverse a trade, just tap the Inverse button underneath the trade ticket.
You'll then be taken to the trade execution page and see the original trade above the entry fields.
Once you're happy with the trade details, just tap "Trade".
That's it, you're done!