[Vuejs]-How can i use vue.js to adjust my side by an url input?

Have you even searched? When you go to the "Get started" section on vuejs.org (https://v2.vuejs.org/v2/guide/) there are excellent examples and tutorials, one of which is https://www.vuemastery.com/courses/intro-to-vue-js/vue-instance/
This will get you a long way creating what you describe above

You don’t need to worry about Node.js or Ruby on Rails.

I’d recommend using the Vue CLI to build your app, because it’ll save you having to worry about all the config yourself. It’ll come with vue-router, which will let you build a Single Page Application. Your header will go in the main App.vue file, and then you can load the body of the page into what’s called the router view.

Have a look at the Vue Router docs which are really good and well-written.