Dating, hooking up, hanging out, etc. are all normal and encouraged activities that are carried out between two adults, especially people of the opposite sex. It is well within the normal activities, if not responsibility, of a man to ask a girl out, but if it is not done well, then it can be terrible.
If you, as a man, have tried to ask a girl out once or twice and have failed, you will understand the gravity of the embarrassment that follows: social awkwardness. That is why a safe bet is to ask a girl out over text. Below are a couple of templates to give you a warm start.
Text templates on how to ask a girl out over text
You ask a girl out over text and she says “NO”
You ask a girl out over text and she says “YES”
To ask a girl out over text you have to be yourself and not be pushy. If you have met her a couple of times take note of her likes, find out if you both have anything in common and use that to find more commonalities to get closer; listen to her comments or recommendations. For example, if she suggests you watch a movie or read a book, you actually doing it has won her heart half way already.
So long as you are not having a face to face conversation with her, she can only imagine your intentions or emotions from the words you write. So be direct, study her interests, find out her likes, man up and give it a go.