Choose your approach (and your approachee) carefully
The medium is the message when it comes to contacting women online, meaning your approach should be tailored to the pathway you'll send it along. For example, the message you send to a woman on Match.com will be different than an @ reply on Twitter, a message on Facebook, an "ask" on Tumblr, et cetera. The method of communication is as important as the message itself. Form is content, fellas.
Facebook is typically the most personal medium because of the level of access, the quantity of photos shared, and the fact that many people's families interact with them there. That's why unsolicited Facebook friend requests will often go ignored.
On the other hand, platforms like Tumblr and Twitter are crafted for the eyes of the Internet at large, and in most cases, interacting with strangers within those communities is the norm. In other words, your random message won't be perceived as out of the ordinary.
Consider the woman in question before choosing your means of contact. Also, notice we said "point" and not "points." It's quality of communication, not quantity, that will get you noticed. Don't go on a Google rampage and start following her every social network profile. That will not land you a date—it will land you a restraining order.