The datasheet for that MCP3002 ADC shows in Figure 6-3, an example schematic of how you might connect the ADC, and how capacitors should be connected to ensure it has a stable power supply. The article you reference is not attempting to sample anything quick (like audio), and the circuit doesn't appear to have any decoupling.
The raspberry-Pi project is sampling a mechanical potentiometer, which can typically change at a few 10's of Hz or less. Their instruction "Slowly turn the trimpot knob and watch the number change. " seems to suggest they may have problems even tracking that. Further the raspberry-Pi project isn't trying to reconstruct a frequency from samples, it is just trying to establish the analogue 'state' for a very slow analogue system. So they aren't very sensitive to huge variation in the sampling frequency; it could vary by 100% and they wouldn't care.
An isolated potentiometer is a simpler electronic environment than you describe, so the electrical noise is likely only the MCP3002. So they may be able to get something usable without proper (normal) decoupling.
However, it sounds like your application may be in a much more electrically-noisy environment, so a good power supply, and hence decoupling will be important. So apply the decoupling capacitors recommended by the manufacturers MCP3002 ADC datasheet.
You likely need to sample at a much higher sampling rate (e.g. at least 10x) than the frequency of the guitar string to make things easier (aim for a much higher sample rate than the Shannon_Nyquist sampling limit). That appears feasible, as the MCP3002 datasheet says 200k samples/second.
A sufficient sample rate alone isn't sufficient. It is also important that the samples are taken at a reasonably stable sample rate. Otherwise it may be too difficult to calculate the actual frequency of a signal from samples when there is unknown sample rate variation (jitter). If the jitter were +/- 50%, that could transpose a note by more than an octave.
Looking at stuff on the Raspberry-Pi's SPI driver e.g. Read data at 2KHz sample rate, how to? it says "Using the current kernel driver, you can perform just over 8000 SPI transactions/sec."
I am not an R-Pi expert, so I would strongly recommend you try to get clarity on this.
However, if that really means 8000 samples/second, then it will be harder to solve your problem using only an R-Pi.
I am not a signal processing expert.
It will be even harder (maybe impossible) if the sample rate has significant jitter. Your code will need a reasonable number of samples to estimate frequency (hence the suggestion for at least 10x samples vs actual frequency). That calculation will be undermined if the actual sample rate varies significantly by an unknown amount. If your goal is to tune within a few % of a specific note, then jitter has to be small enough to enable that.
I am not trying to dishearten you. I am just trying to suggest you consider the whole problem, and not just a small part of it. IMHO, taking a sample of a microphone/piezo sensor using an ADC may be the easy part; it is necessary but not sufficient.
It may be worth using a simpler microcontroller based system, like an mbed, Arduino Duo, etc. to sample the signal, and do initial analysis. The benefit should be much lower jitter, and much higher (than 8000sps) sample rate than the R-Pi appears capable of. This would require you to use C/C++ which may be more work than you are planning.
If you have enough C experience to be comfortable, have a look at mbed.org or higher performance Arduino's like a Due. mbed have a cloud-based compiler, which saves hassle installing tools. You could have a poke around to see if it feels usable.
There are many low-cost mbed development boards. For example the ST Nucleos are under £8 (GBP) +VAT e.g. at Mouser/RS/Farnell/etc. They have, at least, 1msps ADC; the STM32F303 have several 5Msps 12bit ADCs. STM32F3/STM32F4 have hardware floating point, and so might even have enough 'oomph' to solve the analysis part of your project.
I'd recommend sketching out the whole problem, and annotating it with the information you know, or can quickly estimate or discover. This can act as a reference 'scope' so when things change, you can check that you don't forget the knock-on effects.
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Piezo sensors can be awkward to use, and hence the reason people are asking for a schematic, because the output voltage can easily reach above 20V, which might damage the ADC.
You might protect the input of your ADC with e.g. a zener diode to prevent potentially lethal voltage swings reaching the ADCs input.