The first problem is that these sites (particularly the free ones) are going to have a guys to girls ratio of at least 5 to 1, maybe even more. The higher calibre women (in terms of looks and to a lesser extent personality) are going to have in some cases 20 messages a night. They can just pick and choose. So unless you've got a cracking profile, good pictures (and balance, you want one of you travelling, one of you with friends etc), comedy, and ambition, you won't get replies.
Then in to message quality. Anything along the lines of hi how are you doesn't work, nor will the bland nice guy messages focussing on common interests...they get 20 of them a night. I admit I've dabbled in them, the bland focus on common interests I got 0 out of 20 replies, then when I went for flirty/funny/edgy openers, I was getting about 75% replying, think I got 6 in 8. Be different and flirty and curious.
Other problems is timing. I've had conversations with a woman over a night, you'd think naturally she'd continue it the next night if it was her turn to message but once she dropped of the face of the earth, she probably got another 20 messages the following night. Another problem I had was that I was chatting to a girl over the space of a week, I felt 10-14 days was right before I asked her out, and after about 6 or 7 days I never heard from her again, so I'd be tempted to ask after 3-5 days now.
Be flirty. I've had intelligent interesting women talking about sex by the second message if you play it right. Once you get the hang of it its easy to get replies, just flirt your way into a date.
Women have all the power in dating and relationships in their 20s. They are dominant, they say yes or no, and they are kingpin. As men we have to wait until our 30s to have the power in dating and relationships. But most of all, don't take it personally. Often it's just a numbers game, and its about timing. You can see when people are online. One girl was taking 4/5 days to reply as that was when she logged on. It is a bit of fun, but for many its becoming the best (or even the only) way to meet new people. Best of luck.