Why are you inserting yourself into the circuit you are trying to measure? This is like complaining about how you can't get an accurate reading of the weight of some item but insisting on putting one foot on the scale while taking the measurement.
If you want to measure the value of a resistor, then the resistor needs to be removed from any circuit it is in, which includes YOU.
Human body resistance, from one hand to another with dry hands and at the voltages generally produced by a multimeter, tends to be in the hundreds of kilohms to a few megohms when the probe tips are grasped lightly, but can go down to ten kilohms or so if grasped very firmly. Thus, you will greatly impact the measurement of a 1 MΩ resistor, moderately impact the measurement of a 100 kΩ resistor, could noticeably impact the measurement of a 10 kΩ resistor, but probably not, and will almost certainly have little noticeable effect on a 100 Ω resistor.
It sounds like you need to learn a lot more about basic circuit and measurement concepts. You are using meters that are perfectly adequate but, because you are using them improperly, you are concluding that they are broken and must be replaced. What's broken is your knowledge and skill -- but, hey, we were all there at one point and, fortunately, it's something that is pretty easy to fix.
Well, I have basically always held the component and leads at the same time and have measured actually quite a few things over time without ever having an error. One interesting thing here is that I've never really had reason to use more than a 10k resistor, and none of the resistors I've ever measured were really more than that as a result, which meant that touching them or not I never got a different reading, leading me to feel there should be no reason to worry about assembling some kind of jig, while holding the leads all at once I can be very confident everything is touching.
But, at 1meg the problem arises. So, because of the amount of times I've touched the leads with no impact, I didn't think twice about it. Unless I set the multimeter to 20meg, touching the leads just shows o.l, and measuring almost all of the resistors in most basic circuits reads the same touching them or not, which is something I've tested many times. in fact, I think that for like 10 years, I touched the leads and didn't touch the leads every single time I did a measurement, to see no difference, just to check if there was one.
I think for digital circuits, and all relevant values in most "learners circuits" relating to digital electronics, there will be few if any occasions where this problem would arise. (just based on my experiences, since I've never experienced it until now).







