Make a website perform an action on another website?

Not super important goal for this, but I'd like to see it done. So I looked around and found one thing sorta what I was looking for, but it was for how to do it in real-time and not how to do it at all and it ended up not being what I wanted. I am sure I can find the answer, but I just don't know how to phrase the question.

Ok! So my first and maybe for a while (who knows) the last question for this site. I understand coding logic and how it works and all of that and understand a good amount of HTML/CSS/other and stuff tho I mostly work with Lua/JavaScript/C# and usually not on a super professional level as most of it is me just doing my own thing.

Anyway, with all of that out of the way, I would like to know how to make a website perform an action on another website? As in, website A being my own website to connect to website B being a website, I don't own and doing a function on it. I suppose it doesn't have to be one I don't own as I assume it would work the same either way. Let's say on website B there is a red button I want to be clicked but I want website A to do it for me, so I tell website A to connect to website B sorta like how iframes display a website in a website tho I don't care to see it then it clicks the button.

My main goal is to code a trading bot for "howthemarketworks.com" which is a stocks website that allows you to trade fake money in actual stocks to see how well you would do. I want to see how well trading bots even do, as well as improve my own skills. I have no intention of putting it to use on real stocks as I wouldn't trust such a low-level bot with real money and I am sure I could buy/get a real trading bot with advanced algorithms that change based on market conditions if I wanted.

Thanks in advance.