However, I think that basic syntax is rather simple.
You divide entries by &. \ar means arrow. You say the direction by [d] = down, [r] =right and similar.
Images are entered simply by clicking on upload. But I see you have already realized that.
BTW I see that I have in fact drawn a nonsensical diagram.
To include a very simple example, if I just enter A & B I get A and B diagram between them. I can add arrow \ar[r] at A which goes to the right (from A to B). And I can add some caption above or below the arrow.
Yes, there are several manuals for xypic on the internet. Usually, for simply stuff I am able to do without. And if I need something more complicated, I either look into help or copy paste from somewhere (the latter mainly if I drew some similar diagrams in the past).
As you probably know, some people use AMScd. This is supported by MathJax. But no diagonal arrow.
I have heard that tikz is a useful package for drawing diagrams in general. As I have a lot on my plate at the moment, I am probably not going to start learning a new TeX package at the moment.
For commutative diagrams xypic is entirely sufficient for me. For drawing pictures in general, I tend to use metapost.