What is the best advice women would like to give to men on how to approach women?

Approaching girls is a bit of an art.

Here are the 4 big mistakes that most commonly hamper a man's approach:

Waiting for the "right moment"
Not being aggressive enough
Being TOO aggressive
Not closing things out well

... and here are the some steps to take with every approach you make, anywhere:

Spot a girl you want to talk to
There is a form of approaching - usually called "mass approaching" or "shotgun opening" - where you don't bother looking for women you want to meet, and instead you just move through a crowd (usually at a big party or in a bar or nightclub or a very crowded city street or shopping mall) and say hello to and strike up conversations with every woman you encounter.

This usually doesn't work well at all, because your approaches are totally untargeted, and your interaction with each woman is generic and unremarkable. Girls can tell, and that usually means the end of an interaction. If we take the novice baseball player again, the similar example here would be a guy who just swings wildly at every pitch, eyes closed. You're swinging in the dark.

Instead, what you want to do consistently with your approaches is know exactly what girl you're walking up to meet. Is it the blonde, or the brunette? The black girl, the Asian girl, or the redhead? Are you trying to talk to that cute girl who's been staring at you, or are you trying to talk to the entire group of people she's with? (incidentally, I don't have much love for "group theory" - talk to the girl you like, not the group of people she's with.

DON'T make eye contact
Position yourself near her
Pre-open her
Open her
Introduce yourself
Engage in some light banter
Get some early investment
Build some rapport
Close and get out, or move things along

Follow those steps, and you won't have to worry about waiting for the right moment, your levels of aggressiveness will be handled automatically, and you'll know to close things out (or get her moving) as soon as you hit your time limit for an interaction.

Follow those steps, and you get to be a breath of fresh air for all the women tired of being approached by men who aren't following those steps... and are making those big mistakes we talked about not making, instead.