Can you please explain the deposit part of the system, how and where to a user deposits money? Or the company running the server should handle this part?
OT doesn't work that way. It doesn't handle money - just obligations.Another way to think of it is that OT handles liabilities, not assets.
For example, if you are running a Bitcoin wallet on your own computer (Bitcoin-Qt, Multibit, Armory, etc) and you have a balance, there is no counterparty risk associated with them: that balance represents an asset you control.
If you deposit your bitcoins on Mt Gox then you don't have bitcoins any more, you have a promise from Mt Gox to allow you to redeem a balance in their system for bitcoins - your balance on Mt Gox is their liability.
So, if you've got a system that creates liabilities, then OT is superior way to track these liabilities compared to the alternatives. Returning to the previous example, Mt Gox doesn't use anything more complicated than a MySQL table to track its liabilities. They don't give you cryptographically secure receipts, and if they choose to alter your balance (via a simple database command) there's nothing you could do about it. You can't even really prove that they owe you any bitcoins at all, at least for reasonable definitions of "prove".
Mt Gox isn't special in this way - all existing Bitcoin websites work pretty much the same way.
Your original question is backwards then. OT should be used where third parties are already depositing funds in order to add better security and functionality to the situation.
