As of Typescript 2.1 string keys in enums are strongly typed. keyof typeof is used to get info about available string keys (1):

enum Color{
    Red, Green
}

let typedColor: Color = Color.Green;
let typedColorString: keyof typeof Color = "Green";

// Error "Black is not assignable ..." (indexing using Color["Black"] will return undefined runtime)
typedColorString = "Black";

// Error "Type 'string' is not assignable ..." (indexing works runtime)
let letColorString = "Red";
typedColorString = letColorString;

// Works fine
typedColorString = "Red";

// Works fine
const constColorString = "Red";
typedColorString = constColorString

// Works fine (thanks @SergeyT)
let letColorString = "Red";
typedColorString = letColorString as keyof typeof Color;

typedColor = Color[typedColorString];

enum Color{
    Red, Green
}

// To String
 var green: string = Color[Color.Green];

// To Enum / number
var color : Color = Color[green as keyof typeof Color]; //Works with --noImplicitAny

This example works with --noImplicitAny in TypeScript

Sources:

If you provide string values to your enum, a straight cast works just fine.

enum Color {
  Green = "Green",
  Red = "Red"
}

const color = "Green";
const colorEnum = color as Color;

Given you use typescript: Many of the solutions above might not work or are overly complex.

Situation: The strings are not the same as the enum values (casing differs)

enum Color {
  Green = "green",
  Red = "red"
}

Just use:

const color = "green" as Color

Please note that this does not guarantee a valid enum.

Typescript 1.x

If you are sure that an input string has an exact match with Color enum then use:

const color: Color = (<any>Color)["Red"];

In the case where an input string may not match Enum, use:

const mayBeColor: Color | undefined = (<any>Color)["WrongInput"];
if (mayBeColor !== undefined){
     // TypeScript will understand that mayBeColor is of type Color here
}

Playground

If we do not cast enum to <any> type then TypeScript will show the error:

Element implicitly has 'any' type because index expression is not of type 'number'.

It means that by default the TypeScript Enum type works with number indexes, i.e. let c = Color[0], but not with string indexes like let c = Color["string"]. This is a known restriction by the Microsoft team for the more general issue Object string indexes.