The door releases generally consist of a set of metal rods, and the usual cause of failure is one of these becoming detached - does the handle feel loose when you try and open it?
I don't know the specifics for the Suzuki, but door cards are usually held on by a mixture of bolts/screws and clips. The trick is to actually find all the screws... There's usually a couple holding on the handle, one for the inside door release, and three or four in the plastic door pocket.
Once you've managed to find and remove all the screws, you need to remove the inner door release handle (disconnecting the aforementioned metal rod - this bit will be fiddly), then, starting at the bottom, pull the card away from the door to release the clips. With the clips loose, lift the card to unhook the inner window seal from the top of the door frame and remove the card.
Behind the card you'll see a plastic sheet covering the inside of the door, held on with some manky sealant (I don't know what it is, but it's always manky and sticky. Don't get it on your clothes...), and through that you should see holes in the inner door frame. Remove the plastic from the hole closest to the lock and try to find the missing rod. If you're lucky, it'll just need reconnecting.
"Refitting is the reverse of removal", with the fiddly bit being reconnecting the inner release handle.
The process ought to be the same with the rear door, but I've never tried getting the card off a door without opening it. You might find things get in the way, like the rear seat squab... Do the front one first so you know the process, and look at the passenger side door to work out where all the screws are.