HTTP: Type assertion from JSON object to Typescript class/interface

I've reading up on interfaces and type assertion. Been looking at pages like:

I'm getting the hang of it, and it's pretty straightforward in understanding the basics. Though: Nowhere do I find how to type a JSON object to a object I use in my app, when HTTP is involved.

For example, I have an Array of Teacher-objects. Each Teacher has an id, name and an Array of Students. I have another class Students that contain their attributes..... etc.

Somewhere in those links I read that, unless you need to perform actions to an object, it's enough to have just an Interface. But unless you want to do actions to the Object you need a separate class?

My actual Teacher class begins with... :

export class Teacher {

    private students: Array<Student>;

    constructor(public id: string, public name: string) {
        this.students = new Array<Student>();
    }

    public getStudents(): Array<Student> {
        retu this.students;
    }

    public addStudent(value: Student) {
        this.students.push(value);
    } 

    ---some other methods---
}

So as you see, the students array is private in the class and I do have other methods: adding, removing and getting a Teacher by id.

First of all, how would the code look like if I want to cast (or assert the type) the JS object to a Teacher object?

Now my code looks something like this:

Service:

getTeachers() {
    retu this.http.get('someUrl')
    .map((res: Response) => res.json())
}

saveStudent(student: Student) {
    ...
    retu this.http.post('someUrl')
    .map((res: Response) => res.json())
}

Component (Angular 2 Component):

export class ListComponent implements OnActivate {

id: string;
name: string;
teachers: Teacher[];

constructor(public _service: Service, public _router: Router) {

}

routerOnActivate(): void {
    this._service.getTeachers()
        .subscribe(teachers => this.teachers = teachers);
}

saveStudent() {
    let student = new Student(this.id, this.name)
    this._service.saveStudent(student)
        .subscribe(student => this.students.push(student));
    this._service.getStudents()
        .subscribe(students => this.students = students);
}

My interface would look like:

export interface TeacherJSON {
        id: string,
        name: string,
        students: Array<Student>;
}

So obviously I need to first change my teachers array in the component to an instance of my interface? How? Just like: teachers: TeacherJSON[] ??

If the the above interface is not enough to be able to perform actions on the object, how do I move forward? I did lea that you can add methods to your interface like:

interface Thing {
    a: number;
    b: string;
    foo(s: string, n: number): string;
}

process(x: Thing) {
    retu x.foo("abc");
}

I do understand the above example, but I guess the http, mapping and subscribing is throwing me off, and I don't know how to implement it in my code!