What does a vinyl record groove look like?

Am I right when I say the cuts in the 90 degree sides of the groove are then 1 degree of vertical (as you look at a groove from the side)?

What confuses me is I keep reading articles that talk about 22 degree, or 24 degree, or something like that, cutting angles. What is this all about?

The 1 degree angle Neil mentioned and which you have visualized correctly, refers of course to the angle of the edges of the cutting stylus itself (compared to straight vertical). Of course to play a record back most accurately requires that the contact edges of the playback stylus be at the same angle. This ~1 degree angle (cutting or contact edges of styli compared to vertical) is called the Stylus Rake Angle - SRA for short.

That 22/24/etc. degree angle you heard about is the angle of the cantilever when viewed from the side, relative to the horizontal plane of the record. Technically it's the angle between two intersecting lines:
a) the horizontal plane of the record and,
b) a line drawn from the point of the stylus through the pivot point of the cantilever inside the cartridge suspension.

This is called (mysteriously) the Vertical Tracking Angle - VTA for short.

[quote]My whole purpose here is to completely understand how a groove really looks so I can better understand how a stylus can best track that groove.

That is a VERY useful mental exercise. Learning to think like a stylus trying to trace a modulated groove is most helpful. It will save you all kinds of time and trouble when setting up or adjusting your rig (or anyone else's rig for that matter).

The more you listen to vinyl and make adjustments, the more you hear and understand - especially if you work at it. Your ability to hear when something is will improve. Your ability to understand what to adjust, in which direction and by how much is an ear/brain skill. You can develop and improve this skill with practice and reflection.

Go to Vinyl Asylum and read the FAQ's. Most of what's there is correct and all of it is interesting. Jon Risch's article, "VTA once and for all" is especially helpful for understanding the questions you've posed here.

[quote]Not to mention it is flat out amazing to me that all that information can be cut into the groove of a chunk of vinyl in the first place.

On a stereo disc the two groove walls carry related but nevertheless independent signals, each wall undulating at 45 degrees to the record surface. ...

With modulations on one groove wall only... a stylus perched firmly in the groove must move both laterally and vertically.

In stereo recording and reproduction those sounds emanating from the center of the picture are represented by exactly equal signals in the left and right channels, and in accordance with an agreed convention such signals operate the disc cutter so that as one wall goes up the other comes down, resulting in purely lateral groove movement. This of course, is the same as on mono discs, which can be regarded from this point of view as stereo recordings of central sound sources only.