Since any complex collaboration is reducible to the exchange, let's see how Zero Exchange works by examining a simple example of the barter.
Imagine that user A wants to take one pair of valenki in exchange for the 10kg of potatoes. To find the valenki supplier, he have to create the contract and add into it the descriptions of resources 'Valenki' (for consuming) and 'Potato' (for the supplying).
Then user B (the owner of the valenki) sees the appropriate contract in the 'available contracts' list, opens it and adds tenders about his offer (valenki) and need (potatoes).
When user A approves tenders of his partner, the contract became 'Ready' and participants should confirm that they agree with their obligations according the contract. Once the contract is accepted by all participants, it became 'Executed', so participants should fulfill their obligations.
When user receives a good, he confirms the supply and evaluates the resource quality. The evaluation will affect the supplier's reputation.
See the screencast here