I agree that Section 3.7 in The Elements of Statistical Learning is quite confusing. I love this book but hate this section. The PDF available online has this nice Scream pictogram near the section title, so don't worry if you find the math there too complicated.
Here are some other references. There is one book specifically focusing on RRR:
And there is a textbook on multivariate statistics with good coverage of RRR:
Note that this is the same Izenman who has originally coined the term "reduced-rank regression" in
I don't know of a good tutorial paper, but have recently come across this PhD dissertation (that is essentially a composition of three separate papers, available elsewhere too):
Most of it is quite technical, but it can be useful to read the introduction and the beginning of the first main chapter. There is also lots of further references there, in the literature review in the beginning.
I am only giving references here, but I might post a more substantial answer about RRR in your other question What is "reduced-rank regression" all about? when I have some spare time and if there is any interest.