I have been on these dreaded things for about 10 years and I've noticed a few things about what makes women reply.
This thread is going to be honest, some might not like it.
1. Be "hot". Dating sites are shallow and women go for people out of their league.
2. Be rich. See above.
3. Be tall. See above.
(I'm not saying those apply to me. I've blocked plenty of "hot" men for being boring, and ignored plenty of rich men for being annoying)
For most of us who aren't those two things, there are ways that can greatly increase your chances.
1. Photo. From what I've noticed average men tend to have boring photos. Pictures of them indoors in the dark, average quality resolution not smiling, not dressed nicely, just not flattering and they don't stand out at all.
I find myself more inclined to look at someone profile if they have a picture of them doing something interesting, a higher resolution picture, a smiley picture, a more professionally presented picture. It isn't all about face and body. I've looked at plenty of profiles that don't include the guys face at all to find out more.
Good lighting. Happy, fun, friendly, interesting and good quality pictures are what gets attention. Why? They stand out as they are so much different from the rest.
2. Message. Messages saying "hi" "how are you" or paragraphs about the guy in question I am most likely, out of all messages, to ignore. This is a really hard one as a lot of it depends on the mood of the woman in question. It's very easy to ignore people on dating sites when you can't in real life. I wouldn't bother writing paragraphs on anything, either. Waste of time. I don't really have a lot of advice on this, as if your profile sounds interesting they're more likely to reply no matter what it says.
3. Are you what they are looking for?
So many guys make this mistake. They go for people nothing like them, for example, if a guy who works at a gas station messages a university phd student, he is unlikely to get a reply. They are completely different.
4. Your profile.
Don't make it too long, it looks weird. Don't be bitter, it makes people run faster than the face of boo from a wet towel. Be charismatic on messageboards there if you can, girls love a good personality.