Different guides are different because they are by definition, different. No two people do anything the exact same way, and there's more than one way to skin a cat, or test a component in this case, and depending on how accurate a test you're looking to do the more involved it will get.
It should be removed to test it properly, or at the very least have 2 of the 3 leads isolated from the circuit before testing (as in lifting the leads and leaving the tab soldered) so nothing in the circuit gives a false reading.
The quick way is to just test on Ohms and look for a Shorts or Opens. If you have a Short between any 2 leads, 10 Ohms or less, then it's bad, likewise if you have all Open readings between everything then it's bad.
Not all FETs use the same pinout, so it may look the same, but internally it's different. Always look up the part number in question and get the DataSheet for the thing so you know what lead is what.
The DMM has enough voltage to turn on/off the FET under test, so you'll get different readings poking around on it, that's partly normal. For example...
With a good 85N02G N-Channel FET, and the DMM set to Ohms, place the Black test lead on the Tab (Drain) of the FET (pin 2 or 4 depending on the DS you're looking at) then put the Red lead on the Source (pin 3). You should have a High reading (~2M or so) or a Low reading (~500Ohms or so).
If you get a Low reading, them move the Black lead to the Gate (pin 1) and then back to the Tab, the reading should be High now.
If you get a High reading, then move the Red lead to the Gate, and then back to the Source, the reading should be Low now.
For testing a P-Channel FET just reverse the leads.
Testing it on the Diode/Continuity setting will net roughly the same results, but your DMM might squeal for the Low reading. That doesn't necessarily mean it's a short as they all have a different threshold for going off, some will go off at 300 Ohms, which is why using the Ohms setting is more accurate in this case, but if you have it squeal testing between multiple leads in both directions then it's most likely shorted, but again the Ohms setting is the easier way to tell if it's really a short, or just a 200 Ohm reading, which isn't a short.
What all of this is not going to tell you though is if the thing is breaking down under load, but if you have more than one FET of the same type then you can compare them and if the differences between them are too great then just replace it, putting in a new part that it doesn't need isn't going to hurt anything but your wallet, or you can build up a test circuit for it and see how it acts under load, cheaper to just replace it though if it's suspected to be bad.