ive never taken the central locking off my fiesta but i have on ford escorts and i would guess that the way it works is the same.
it sounds like you have a sticking motor or faulty motor on the central locking.
first you should find what side is causing the problem this could be done by removing one of the door cards and disconnecting the wires to the central locking then using the buttons on the key to lock / unlock.
if the the door that is connected works correctly then replug in the wires and do the same to the other door.
once you have located the faulty central locking motor you can remove by taking the top screw out (see pic) which will remove the cover that covers the lock you may have to take the lock it self out which is held in by U shaped bit of metal with a lip on it you pull this away from the lock also remove the round plastic switch that is around the lock i think its got a clip on it some where.
the three screw that hold the catch / central locking are normally very tight so make sure you have a good screwdriver.
after you remove those three screws the catch / central lock should come out.
this pic is of a Ford Escort catch / central locking but i would think its either very similar or the same as the fiesta.
you may be able to get another central locking motor from ebay if you search for "fiesta breaking" and email the seller and ask if you post abroad.
also remember if you buy apart from the UK then our cars are right hand drive so dont ask for the drivers side or passenger side because it will be for the wrong door.
if you cant buy one from ebay you could try DIY Motorist
and email them and ask if they will ship abroad. i know one of the people who works there and the last time i spoke to him he told me they were starting to use ebay to sell so i guess they must be posting stuff.