How can I keep up a conversation with someone new, you've met on a chatting page?

Hi! Just keep casual conversation, until you get to know her better. Ask how she's doing, what she's up to, about her family, favorite hobbies, etc. Also, one big tip, is to address the awkwardness. Like if you don't know what to say, if you're tongue- tied, address it. It'll make it less awkward in the moment. Hope this helps!