Want actual instructions? This is the way I would do it:
Build a linear actuator. I happen to like this company and some of their stuff.
Don't use an Arduino, use a Raspberry Pi. Connect it to the internet. Install Node.js on it.
Create a Node.js application using the Johnny-Five library to control the motor
Create a Node.js application using Express to set up a web app that can control the motor
You'll need to know electronics so you can work the motors with Johnny-Five and enough JavaScript, HTML, CSS to set up the web server as the interface. JavaScript you can learn from Eloquent JavaScript Chapters 1-6. It's a book but it has a whole lot of personality. HTML and CSS I would recommend Scrimba's interactive video tutorials, you can literally edit the code in the tutorial live to experiment if you pause the video.
