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I'm kind of new to sound. I'm trying to edit an instrumental piece to cut out a section of the piece but keep the song flowing smoothly. To do this, I need to make my cuts as exactly close to the beat as possible. When looking at a waveform graph of a song, what part of the graph is the beat? Is it where the line crosses the equilibrium point? Or is it at a peak in the waveform? I have looked thoroughly for the answer to this, but I haven't been able to find anything. Maybe I'm just not wording it correctly.

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Generally, the trick is to cut at the quietest point, just before the beat, where the waveform crosses the zero line.

If your beat is a kick drum, that's usually the simplest to find, it will form the biggest wave shape at the lowest obvious frequency.

Back in the analog tape days, you'd shuffle the tape back & forth until you could hear that slow thump, slide the tape to just before it, make your marker, then make your cut just before it & hope it worked.
These days you can pretty much see it, cut, listen, change your mind, repeat until you get it right.

...but the principle is the same - pick a point just before the beat & no-one will notice, so long as there are no major instrumentation/ambience changes at your edit point.

An example - just a random waveform I picked off the web - cut at one of the points marked in red - where the sound has had longest to fade away beforehand, right before the main beat happens.

Note: by "beat" it doesn't have to be right "on the one" of the piece, sometimes cutting at a non-important [yet still easy to see on the waveform] beat can be more effective.

Experiment.

enter image description here

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You generally have to have a sense of rhythm to find the down beat accurately. Have a metronome in your head and approximate the BPM of the song, then preview the song in an audio editor such as Audacity. Allow the metronome in your head to follow the preview bar in the audio editor, and approximate where the beat lands.

Then zoom in and locate where in your approximation you could choose a more accurate down beat.

Here's an example waveform, where I've marked two down beats:

And zooming further in shows how each part of the waveform looks at the down beat:

Lower frequencies (e.g. bass, as opposed to treble) have longer wavelengths, and thus, the large influence of the key down beat element should be noticeable on these images since the wavelength is relatively long.

You should, however, note that it's not necessarily obvious where the down beat is, but in general, a loud transient like a kick drum (in the case of my example, a cinematic slam) tells you where the down beat is. Use your ears, and like I said, take the time to zoom in and locate where the down beat is.

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