There are two basic situations in which you can ask someone out.
The first is when you are seeing each other regularly. This is when you can do stuff like “make her comfortable, relaxed and be open about what she thinks when I ask her out.”
The second is when you are not seeing each other regularly. Here you do not have time for planning and just need to take advantage of an opportunity when you see one. You can’t afford to overthink in this situation.
You just walk up to her, say hi, and talk until one or both of you have to go. This should be easy if you have a pre-established relationship. If you don’t, then you probably shouldn’t ask her out. When it comes time to part ways, say you’d like to get to know her better and if she would be interested in going out on a date with you. I like to specifically use the word ‘date’ so there’s no misconstruing your intentions. You don’t want to get to the end of a date and realize that she thought you guys were just hanging out as friends.
If she says yes, then the hard work is done and the rest is coordination.