How to declare Return Types for Functions in TypeScript

You are correct - here is a fully working example - you'll see that var result is implicitly a string because the return type is specified on the greet() function. Change the type to number and you'll get warnings.

class Greeter {
    greeting: string;
    constructor (message: string) {
        this.greeting = message;
    }
    greet() : string {
        return "Hello, " + this.greeting;
    }
} 

var greeter = new Greeter("Hi");
var result = greeter.greet();

Here is the number example - you'll see red squiggles in the playground editor if you try this:

greet() : number {
    return "Hello, " + this.greeting;
}

Return types using arrow notation is the same as previous answers:

const sum = (a: number, b: number) : number => a + b;

functionName() : ReturnType { ... }