Appending data to a web page from a form using a JavaScript class
The convention with class names is that they are usually written in pascal case, for example, PascalCase. So you should use Data for your class name.

While it's great that you're experimenting with javascript classes, I feel that they're not the right tool to use for this. The main idea of a class is that they can be used to create multiple objects based off the class. 

Here's a pseudo-code example of when using a class is ideal.

class Vehicle {
    constructor(model, regNumber) {
        this.model = model;
        this.regNumber = regNumber;
    }

    start() {}
    accelerate(acc) {}
    brake() {}
}

class Car extends Vehicle {
    // additional methods
}

const ford = new Car('Ford', 'HR28AP0000');
const auto = new Vehicle('ExampleDX', 'TN09XX0000');


The vehicle class has some attributes and methods. This example lends itself very well to the idea of classes. 

For your code, it's best to use an append function instead. 

I'd suggest looking up Object Oriented Programming. Some well written books and blogs will do a much better job of explaining when and where to use classes and objects and other OOP principles.

Edit: About try-catch, it's common to throw an Error object or one of it's descendants. 

if(email == '' || url == '' || number == '' ) {
    throw new Error("Empty");
}