I'm not a lady, but quite simply... Don't play games. There won't be a one size fits all answer. Read the profile, and when you think you are ready to message someone, read it again. Type a message based on the person, and then read the profile and rework your message.

It sounds silly, but you don't walk into a job interview in ruined clothes do you?

Then put the best foot forward that you can in the online dating realm. Actually pay attention to the profile, and if you are just messaging a gal because she is "hawt" then consider moving along without messaging her.

I can't say what exactly TO write, but here's a list of stuff I don't answer kindly to:

"How much does a polar bear weigh? Enough to break the ice, hurr hurr!"
"Show me your tits."
"We should text!"
"Do you wear your glasses during sex?"
"I want to cum on your glasses. So bad." - Yes, some guy actually said this to me on a site as an introduction. He got a rude response and a flag.

Be yourself, ask a question after you read her profile. MrWilly had some good advice.

Be honest and go with the flow.
Have fun, but be careful about anyone you go out with.
Good luck!