How do I define a method in Razor?

Leaving alone any debates over when (if ever) it should be done, @functions is how you do it.

@functions {

    // Add code here.

}

You mean inline helper?

@helper SayHello(string name)
{
    <div>Hello @name</div>
}

@SayHello("John")

It's very simple to define a function inside razor.

@functions {

    public static HtmlString OrderedList(IEnumerable<string> items)
    { }
}

So you can call a the function anywhere. Like

@Functions.OrderedList(new[] { "Blue", "Red", "Green" })

However, this same work can be done through helper too. As an example

@helper OrderedList(IEnumerable<string> items){
    <ol>
        @foreach(var item in items){
            <li>@item</li>
        }
    </ol>
}

So what is the difference?? According to this previous post both @helpers and @functions do share one thing in common - they make code reuse a possibility within Web Pages. They also share another thing in common - they look the same at first glance, which is what might cause a bit of confusion about their roles. However, they are not the same. In essence, a helper is a reusable snippet of Razor sytnax exposed as a method, and is intended for rendering HTML to the browser, whereas a function is static utility method that can be called from anywhere within your Web Pages application. The return type for a helper is always HelperResult, whereas the return type for a function is whatever you want it to be.

You could also do it with a Func like this

@{
    var getStyle = new Func<int, int, string>((width, margin) => string.Format("width: {0}px; margin: {1}px;", width, margin));
}

<div style="@getStyle(50, 2)"></div>

Razor is just a templating engine.

You should create a regular class.

If you want to make a method inside of a Razor page, put them in an @functions block.

You can also just use the @{ } block to create functions:

@{
    async Task<string> MyAsyncString(string input)
    {
        return Task.FromResult(input);
    }
}

Then later in your razor page:

   <div>@(await MyAsyncString("weee").ConfigureAwait(false))</div>

MyModelVm.cs

public class MyModelVm
{
    public HttpStatusCode StatusCode { get; set; }
}

Index.cshtml

@model MyNamespace.MyModelVm
@functions
{
    string GetErrorMessage()
    {
        var isNotFound = Model.StatusCode == HttpStatusCode.NotFound;
        string errorMessage;
        if (isNotFound)
        {
            errorMessage = Resources.NotFoundMessage;
        }
        else
        {
            errorMessage = Resources.GeneralErrorMessage
        }

        return errorMessage;
    }
}

<div>
    @GetErrorMessage()
</div>

You could also use the code block below. It is much cleaner and has more functionality. You can also insert variables above and functions below. Instead of using 2 seperate code blocks.

@{
    string exampleVariable = "just an example variable";
    string anotherExampleVariable = "just another example variable";

    string GetErrorMessage()
    {
        var isNotFound = Model.StatusCode == HttpStatusCode.NotFound;
        string errorMessage;
        if (isNotFound)
        {
            errorMessage = Resources.NotFoundMessage;
        }
        else
        {
            errorMessage = Resources.GeneralErrorMessage
        }

        return errorMessage;
    }
}

Here is how the list helper is written in ASP.NET Core 3

You can now include HTML markup in the body of a method declared in a code block as a local method as previously, or in an @functions block. The method should return void, or Task if it requires asynchronous processing :

@{
    void Template(string[] listItems, string style)
    {
        <ul>
            @foreach (var listItem in listItems)
            {
            <li class="@style">@listItem</li>
            }
        </ul>
    }
}