How to step up a conversation with girl i'd ideally like

Be specific, it shows you're engaging with what they're saying. Ask them about specific things you know are going on in their life from either previous conversations or what you can ascertain from their profile.
Show that you're thinking about them, but not in a way that is too intense. For example, "There's this song that I thought you'd like."
Find out what their interests are/what shows they like/bands they listen to and check them out. Give your opinion on them, ask about what they think of certain aspects.
Use topical events as a conversation starter, this can be done best if you know their political views.
Incorporate jokes or themes from previous interactions into what you're saying, to put across that you value the conversations you have with them.
Once you've gotten more comfortable, try for some friendly teasing, keep the flirting subtle and don't say anything outright like "I'm so horny," instead imply it, like "I've been thinking about you all day." In terms of compliments a simple "you're pretty," will come across as too impersonal, so go into detail, like "you have such cute dimples/freckles," or "you have amazing eyes." Try to get them to think of you naked, ignore a message and then come back later like "sorry, was in the shower".
Basically just be subtle and try to be specific to them, so it seems like you're paying attention.
Especially in the beginning don't send more than two messages in a row without a reply.

op give up online stuff and start talking to them in person

>>25275901
ignore this guy he is a speg

"I've been thinking about you all day" makes her think you are a creep/weirdo/clingy unless you are already dating

>>25274664
"I'm heading to XYZ pub tonight. You should join me for a drink"

if you havent met this girl irl before messaging her on fb is going to be fruitless

given that you're asking /soc/ for help you're too autistic to pull it off either way