Wire them in parallel. Do you know how to wire a single door bell? If so, then just repeat with a second set of cable to the other door. I'm not very good at drawing. Depending on the layout of the property you should be able to combine any double-runs of cable back to the transformer or bell into a single cable. You'll have to draw that bit out yourself as I don't know the property layout.
Yes, stateit is correct. You wire them in parallel, I did mine last year. If the second bell isn't loud then swap the 2 wires around that connect to it.
Just wire each bells back to the push as if there were two pushes, but only using one push, so two wire to one connector and two to the other.
Ian, wireless really does make more sense here. If the one you bought didn't work properly, there will be a reason; either it's pants, faulty, the signal is interfered with by summat like RSJs, aluminium-lined p'board, or summat else, or your batteries are flat, or you haven't switched them to the correct frequency... Basically, wireless does work, so you can make yours work too. However, if you are determined to go the wired route, then simply wire up one bell to your button and then take the 2-core 'push button' wire from the second bell and connect it to either the first bell or the push button - whichever is closest. How to wire? The two wires from the 2nd bell go to the exact same terminals as these wires of the first bell; they join them in the terminals. But, you'd be nuts not to go wireless in this case. Nuts I say...