Financial arrangements vary, I suspect, but the general idea is that the airline selling the ticket functions like a consolidator. They buy a number of seats at a bulk rate. If they can sell individual tickets at a sufficiently high price, they profit.

It works the same way as when a manufacturer builds an appliance and puts Kenmore's name on it. They get to sell a bunch of them at a wholesale rate to Sears, and Sears profits (or not) from selling them at a retail price. (OK, maybe that's an US-specific analogy, I don't know if you have Sears in the UK, but you get the idea.)

In many cases the second airline adds value. AA, for example, codeshares on TK flights between IST and the US. Because of its brand and its FF program and the fact that US-govt-funded travel must be on a US airline (code-shares are OK), AA is able to sell seats at a higher price in the US than TK can get for the same seat.

Alliances such as NW/KL are more complicated, of course, with code-sharing being only a part of a larger deal.