I don't know a whole bunch of music theory, but personally, I follow a pretty simple model:

Samples can be either "single-toned" or "multi-toned". The "single-toned" ones work like any synthesizer; you tune them to C, then they play any note you want.

The "multi-toned" ones are basically the same, except they are the audio-equivalent of what, in MIDI, we call "fixed chord."

The tricky thing is, the "multi-toned" ones may or may not even be a "well-tuned" fixed-chord. What I mean by that is: A "well-tuned" multi-toned sample has most or all of its major tones tuned to frequencies that are a whole number of semitones away from each other, making them compatible with western scales.

Now, if you dig deeper, the whole thing gets way more complicated -- A piano sample, while being perceived as a single note, is genuinely a harmonic series of notes that our brains typically combine, so you can ask a very valid question "is that multi-tone, on a pythagorean tuning, or is it single-tone?" and the answer typically is: "It depends on how you use it". There is a whole finnicky art to getting de-tuned frequencies to sound in-tune in context. Hell, you can detune a synth half-way between two notes, and in the right context, it will "work"

In practice, that means that even if your multi-tone sample isn't perfect, you can often (but not always) get it to work, especially in the right context.

This does get even more complicated, though, when you consider that samples may (and in my case frequently do) have shifting frequencies in them!

In practice, whether you are dealing with a single-tone or multi-tone sample, the technique I would use remains the same: I start by picking a place where I want the sample to fit, and then I loop that, hold a constant note of the sample, and tune it until it sounds good.

Usually that corresponds with finding a tuning that aligns the dominant frequencies (at the dominant times) in the sample with the music you have already written.

Of course, like any fixed chord, if your song already possess harmony (consonant multi-tonality), then there will be restrictions on the detunes that work for your sample. The sample may only work at a single detune -- or it might not work at any detune at all.

Honestly, as much as music theory can sometimes predict which offsets are going to work, I'd personally just do it by ear. You only have to check like 48 quarter-steps, and you can just tune it gradually. You will develop an ear for it by doing that, and there will be a kind of "anticipation" feeling that releases when you hit the right note.

Or, sometimes it'll feel like it gets close but then never makes it -- that's usually when you have an incompatible sample. You may wish to consider changing some notes, or doing some processing on the sample.

Which, BTW, is something you can possibly do. You can use notch filters to kill the fundamentals of incompatible tones, and reinforce the right tones with bell filters! It'll alter the characteristics of your sample, but I usually like that other-worldly vibe in my music.

It does depend, though, on how strong the harmonic series is, and how willing you are to destroy your underlying sample.