I can imagine the man pages are a bit overwhelming and do do really tell how to use grep. Grep and egrep is all about finding regular expressions.
Grep and egrep differ in how they handle regular expressions. Grep handles normal regular expressions, egrep handles extended regular expression syntax. Those are similar, but not identical. Extended regular expressions is a new definition which is not upward compatible with normal regular expressions. There is at least one case I know where a sequence in extended regular expression is the opposite of the same sequence in normal regular expression.
Differences between the two are pointed out here:
https://www.regular-expressions.info/posix.html For more information on how to use grep, google for "regular expressions", not for grep.
grep -E is identical to egrep, it make grep to use extended regular expressions.
jlinkels