How should I introduce my 13-year-old daughter to programming?

I'm recommending some video games like Human Resource Machine: https://store.steampowered.com/app/375820/Human_Resource_Mac... It's always fun to "see" the logic being executed and have fun challenges.

On the next step, I believe things like Scratch are pretty good to introduce to programming.

On the web development part, I built a little "game" as a tutorial of my tool: https://luna-park.app/challenge . It's JS with visual nodes, this is used to learn algorithmic for students.

My son is 14 and I got him interested by showing him how to automate navigating web pages with selenium.

We used python as that’s what they teach in school, and was happy with an app that that navigated to Deliveroo and added his favourite McDonalds order to the cart!

You'll find that when they teach kids in the schools, they start with the fundamentals. Logic, branching, loops, problem decomposition, debugging. Doing so has even been shown to improve their overall academics because they approach all their classes with an eye to logic and troubleshooting when they get things wrong and it builds resilience and self-correction into their world views.

Even aside from that, it puts them in the same boat as experienced coders, in making their own decisions -- If they know the logic, they can choose for themselves whether they prefer the syntax of Python vs. JavaScript, or any other environment.

Let her do something visually compelling in a medium she already uses to engage with the computer.

I've enjoyed success in getting people excited by having a person create an HTML button, and write a line of JavaScript that changes the background colour of the page to their favourite colour. After they have done that, and as such feel like a god, then some fundamentals via simple games.

What interests her? What excites her? My philosophy of childhood education mostly comes down to inspiring and growing their curiosity. If you can guide her to things that are most interesting, over time she will become more interested in more complex, robust things and will need your help navigating how to do those things.

When I was in 3rd-5th grade I really enjoyed scratch. In middle school I started learning python mostly on my own. I found how Python did classes/OOP extremely challenging and confusing to my middle school brain, but it was pretty simple otherwise.