You must have a charger that can output 2 Amp current. This is obviously, the easy part.
Then the cable must be thick enough to not drop voltage. Ordinary USB cable (for 1A chargers) won't do 2A fast charging even used with a 2A charger. For a 1 meter long cable, 12 AWG wires are enough (I did not test lower AWG or longer length).
Now the last part for conducting a true fast charging for S4 and Note 2: the D+ and D- pins need to be shorted. Samsung is now compatible with iDevice, i.e., the D+ and D- can also be set to either 2.8V and 2.1V (for iPad) or 2.1V and 2.8V (for iPhone). If you make your own cable, you don't need wires for these two pins, just two wires are enough (for V+ and V-, respectively), but you must short these two pins on the micro USB plug (i.e. on the phone side, not the charger side). Fortunately, most fast chargers fit these conditions, as you'll see shortly.
To test current, use a Kill A Watt. Read watt, not VA, then divide it by 5 to get the charging current. For example, the reading in this photo is 10 watt, so the charging current is about 2000 mA.
If you don't have a Kill A Watt, you may use the Battery Monitor Widget by 3c. Note that such apps cannot read realtime charging current. You have to set the history update rate to 60 seconds or so and mA retrieval method to estimated, then you can see estimated charging current in history like this:
Fast charging is activated only when battery level is below 80%. At higher level, current is reduced to 1200 mA and lower:
When screen is on, charging current is reduced from 1900 mA to 1200 mA:
Now let's see which 2.1A rapid chargers can really do full speed fast charging for S4:
This $5 MERKURY 2.1A rapid charger found in Ross is the cheapest one that can really do fast charging for S4 (cable not included):
This cheap dual-port Case Logic also works perfectly with S4, with either ports. Again, no cable included. This is my favorite charger - very slim, the color shell can be easily removed, see above photos, making it even slimmer, and the case can be easily opened with two screws to do any mods:
This Innergie PocketCell 3000 mAh power bank can really charge S4 rapidly, thanking to its 2.1A output which is very hard to find in power banks - most of them can output only 1A or less. It charged my S4 from empty to 82% in one hour and 20 minutes before itself was totally depleted. It is currently on clearance in RadioShack for $15, a steal.
This DigiPower Home and Car Power Kit can also charge S4 in full speed at 1900mA, if you use a right USB cable. With the cable included in the package, you can only get 1600 mA at the best.
So, finding an inexpensive fast charger is easy, the real challenge is to find a high-current USB cable. If you can find one that can do 1600 mA, you are lucky. Like the DigiPower, Almost all 2.1A rapid chargers come with either a crappy cable that cannot do full 1900 mA, or no cable included at all like the Merkury and Case Logic.
How fast is fast charging? About 1.3~1.5 hours vs. 2.5~3.5 hours. Something once you experienced, can no longer live without.
If you are buying a charger, pick up a 2.1A one. Even if you cannot find a good cable to get full speed @1900 mA, 1600 mA is still much faster than 1A. When buying a power bank, don't just read the mAh, also make sure it can output at least 2.1A!