Either your version of the docs is old or you have to read a bit more. The docs of perl 5.6.0 state the following:
m Treat string as multiple lines.
That is, change "^" and
"$" from matching the start or end of the string to
matching the start or end of any line anywhere within
the string.
s Treat string as single line. That is, change "." to
match any character whatsoever, even a newline, which
normally it would not match.
and the next paragraph explains it even further.
I had problems with perldoc too, when I started to learn perl.
For a beginner the best she/he can do is buy the camel book.
But for a quick lookup of syntax the best is perldoc!