Disclaimer: I am so not an expert at this, but I do do somethings that work quite well. I am just gonna write as it comes to mind, so hope something clicks for you.

How to engage in conversations: I always make comments about the situation and just let the words out. Regardless of whether I get a response or not. In my experience, situational and observational starters are the best and the most low risk.

For eg. I enter an elevator, and another girl is there, I usually say something along the lines of "God I am having such a shit week, I can't wait for the weekend" and just smile. If she reciprocates, I go "Please tell me your life is not like that" or something along those lines. That way is she doesn't respond, she feels the pressure, not me.

I also go, "Oh I haven't seen you before, you work here?" ... "Nice, etc etc, see you around".

The aim is not to close her, but just be able to start conversations wherever I go. Once I became super comfortable with this, I've been able to get numbers quiet easily literally before the elevator doors open up again.

One way to continue conversations when the conversation is feeling dull is to ask the most random questions, I usually go with, so who do you think would win in a fight, me or your boyfriend? It doesn't matter what she responds with since I am gonna tease her regardless of what her response is. Also can find out what her relationship status is etc. Just make comments about things you find interesting or funny. Practice free word flow and ask questions or make statements that warrant a reaction.

How to be funny? Misinterpret and exaggerations. These two are my most go to methods and I am considered quite funny by pretty much all those that interact with me. My sense of humor can be a bit too much, but then again helps in filtering out people I wouldn't connect with down the line anyways.

Watch a ton of stand up coming till you understand this is what most of them do. They misinterpret and exaggerate situations.

This video breaks down comedy really well imo; https://www.youtube.com/watch?v=ufdvYrTeTuU

How to get a number? This is my go to move to get a number. Once the conversation is in flow, I say "We should continue this conversation once I am not so busy etc" if she says "Yeaa"

I just take my phone, open the phone dialer and hand it to her. If done very causally, they almost always give me their number. Also once the phone is in their hand, I don't hover over their shoulder, I legit look somewhere else or just appear busy.

How to hold hands? During the middle of a conversation, I go, dude, how big are your hands? and then open my hand waist high, usually they do the same, I say let me compare..put my hands on top of theirs and just interlock fingers gently..if they don't pull back I keep it there and lead her somewhere then let go. Simple, yet quite effective in my experience.

That's all I could think of for now, do hope this provides value to someone and maybe even learn more suggestions from you all.