How to authenticate in ASP.NET WebApi using [System.Web.Http.Authorize] attribute?

Question

ASP.NET

Hello.
I have a method in a WebApi controller which looks like this:

[Authorize]
public string Get(int x)
{
    return "Hello";
}

The server also has a database with logins and passwords, authentication methods, Membership and Role providers, etc. mechanisms that can authenticate a user by login and password.
And here are the questions:
1. With the help of what code (what should be done on the server?) I can send something to the client (for example, a token) so that his requests to the specified method on the server are authorized by the [Authorize] attribute
2. What should be sent to the server from the client side (Windows Form application) (preferably using RestSharp) so that the request passes authorization?
My assumptions:
Perhaps there is some way, such as FormsAuthentication.SetAuthCookie(UserName), which generates a token that needs to be passed to the client and the client, adding it to its header, will automatically be authorized through the internal mechanisms of ASP.NET. I wonder if this approach can be used?
Thank you for your attention and your tips, answers, help...