Diagnosing puffers requires a little research and methodology.  Haste is often the largest obstacle to overcome, as we sometimes seek out the path of least resistance and search for quick answers. There are many variables at work here, so taking an holistic approach (there's that word again) to diagnosis and treatment is imperative.  When the disease and/or illness is treatable, it does you no good to treat symptoms without taking care of what got your fish sick in the first place.  For some diseases and/or illnesses it's quite obvious what the problem is, and how to treat it.  There are times, however, when you may be stumped.  It is at this point that systematic diagnosis is especially applicable.  Here is a guideline methodology you can use to diagnose and treat your puffer(s):
 

1.  IDENTIFYING THE SYMPTOMS
This is the simplest step.  You're basically going to note what abnormalities your puffer is exhibiting.  Don't underestimate this though.  Be thorough in your appraisal of symptoms, as some are more subtle than others.  It's important to note them all, since there may be more than one disease or illness afflicting your puffer at the same time.  For example, it's not uncommon to find that parasitic infections are often coupled with secondary bacterial infections.  In that case, you would be dealing with the parasite and the bacteria in question.  Once you have identified the symptoms, you can go on to figuring out what the particular disease or illness is.

2 & 3.  IDENTIFYING THE DISEASE OR ILLNESS AND ITS ORIGIN(S)
Sounds simple, right?  It really isn't that complicated, but as previously mentioned it requires some methodology.  The main problem with properly diagnosing puffers is that many ailments share the same or very similar symptoms.  It is often best to make a list of possible ailments and go through them, systematically eliminating them as you go along.  This process of "ruling out what it isn't" is a sound way to start.  Start broad, then work your way down to specifics.  This is applicable in the first step of this subsection.  As you rule out what factors aren't contributing, you'll eventually be left with your answer.  Remember, there may be more than one pathological factor at work in your tank.

a. Rule out environmental factors.  Test ALL water parameters: ph, temperature, hardness, ammonia, nitrate and salinity (if applicable).  If you want to be especially thorough, also check for phosphates and dissolved organics.  All of these tests should be available at your LFS.  Take a look at the tank decor, and make sure all the items are made for the aquarium.  If you have purchased fake wood and the like from your LFS, hopefully you've checked the label to make sure it's ok for fish.  Some decor is meant for reptiles and the like, and is treated with antibacterial agents which are toxic to your fish.  After gathering your water readings, take a look at  the Species Specifics page to make sure your tank is within acceptable tolerances for your species of puffer.  Check your filter(s) as well.  Make sure they're clear of fungus or algae, as photosynthesis can have an effect on your ph.  This is actually a good example of why it's important to know the origin of the illness. (e.g. If your puffer is ill because of extremely high ph, you may just go ahead and lower the ph using chemicals.  In the long run, the ph will rise to toxic levels once the algae in your filter grows thicker.  Without knowing what's causing the adverse condition, you're applying short term solutions to long term problems.)  Additionally, think of any other environmental factors which may be contributing to your puffer's poor health. (lack of water changes, excessive detritus in the tank, lack of gravel vacuuming) If you cannot rule this out, this is the culprit.  Make the appropriate changes to your water.  Remember to make those changes SLOWLY, over a period of days, not hours (with the exception of ammonia).  If you are proceeding to the next section, you have determined that poor water quality is NOT causing your fish to be ill.

b. Rule out biological causes.  Most biological pathogens can be observed externally.  There are, however, a few which can only be observed indirectly.  Those who make their presence known indirectly do so by causing certain symptoms to develop, such as overproduction of the slime coat, or red streaking on the body of your puffer.  You may refer to a good flowchart that has pictures of the parasites or their symptoms for reference.  If you don't have access to such material, you can view a flowchart here.  You can also go straight to the Puffernet Diagnosis and Treatment page by clicking here.  Biological causes will, more often than not, fall into one of these categories: parasitic, viral, or bacterial.

c.  Rule out mental (stress-related) causes.  Stressors in pufferfish can often lead to illness or disease.  Stressors are, at the risk of being redundant, things which cause your fish stress.  Things like poor water quality can lead to susceptibility of puffers to parasitic infections.  Depending on your puffer, things outside the tank may frighten it constantly.  Tank partners may also be a factor, especially when it's another puffer bullying it.  You can view some of the symptoms of overly stressed puffers and their probable causes here.

There will be times when none or all of the above seem applicable.  Is it possible your puffer has some kind of congenital defect?  Yes, but not likely.  Puffers endure long trips to make it to your LFS, and only the stronger ones make it.  Go back and rethink the factors involved.  Get a second opinion from people who know and keep puffers at newsgroups and clubs.  Due to the amount of variables involved, it's quite likely something was overlooked in the process.

4.  TREATMENT AND ERADICATION OF THE DISEASE/ILLNESS
Now it's time to act upon your diagnosis.  If the water quality isn't within the right parameters for your puffer, change your water chemistry.  Again, the key here is to change those levels SLOWLY.  I can't stress this enough.  You must do this over days, not hours.  For example, changing the ph of your tank more than .3 units per day is stressful to puffers.  Although many are adaptive to changing water conditions, they just can't handle such extremes.
If your puffers are stressed, remove the stressor.
If you have a biological pathogen, refer to the flowchart or check the database for treatment information. They are interlinked, with the database supporting the flowchart.
After verifying your diagnosis, you can get some information on the various medicines available on the market at the Rx database.
* Try to seek out a non-chemical cure first.  It's always best to treat your puffer's ailment without chemicals, if at all possible.  Temperature, ph, and salinity may cure some diseases.

Diagnostic Methodology

Diagnostic Flowchart

Pathogenic Database

Rx Database