Write an article based on this "Understand the root of the problem. Observe replaced transformers. Verify the condition of external fuses, if necessary. Check for overdraw on your secondary. Remove inputs and outputs to determine the source of the failure."
Transformer failure is usually a symptom of a different kind of failure somewhere in the electrical circuit. Transformers generally have long lives, and rarely burn out by themselves. If the problem causing your transformer to short out is coming from elsewhere in your circuit, it's likely the transformer will burn out again. After you've replaced the transformer, observe it to make sure this does not happen. If it does, you'll need to perform additional tests. An overloaded transformer will often make snapping and crackling noises. If you hear sounds like these, cut power to the transformer to prevent burnout. If your transformer has an internal fuse, you may not have fuses in the line leading up to the transformer. Otherwise, there should be fuses in the power supply line to the transformer. Check to make sure these are in good condition and replace any that aren't working properly.  Blackness, melting, and deforming in fuses are good indications that the fuse has been damaged. Simple remove and replace these. In some cases, it might be hard to tell if a fuse is in good condition. Attach your DMM to the fuse with one lead on each fuse end. If current runs through the fuse, it's good. In some cases, the secondary of your transformer may be drawing too much current, causing it to short out. If you have a multi-tap transformer and you receive the reading "OL" from the secondary, it's likely the secondary is shorted.  Test this by hooking up the secondary to its circuit and using your DMM to test the secondary lines. If the reading is above the amperage rating for the transformer, the circuit is drawing too much power. Many common transformers have 3 amp fuses. The amperage rating for your transformer fuse may be labeled on the transformer, but will also be available in the circuit schematic. For linear fuses, you'll only have one input and output. In this case, your trouble is either coming from the input circuit or the output circuit. For more complex fuses, remove inputs and outputs to the transformer one by one to determine what component of the entire circuit is causing the short.