Do:

var isTrueSet = (myValue === 'true');

using the identity operator (===), which doesn't make any implicit type conversions when the compared variables have different types.

Don't:

You should probably be cautious about using these two methods for your specific needs:

var myBool = Boolean("false");  // == true

var myBool = !!"false";  // == true

Any string which isn't the empty string will evaluate to true by using them. Although they're the cleanest methods I can think of concerning to boolean conversion, I think they're not what you're looking for.

The strict equality operator (===) behaves identically to the abstract equality operator (==) except no type conversion is done, and the types must be the same to be considered equal.

Reference: Javascript Tutorial: Comparison Operators

The == operator will compare for equality after doing any necessary type conversions. The === operator will not do the conversion, so if two values are not the same type === will simply return false. Both are equally quick.

To quote Douglas Crockford's excellent JavaScript: The Good Parts,

JavaScript has two sets of equality operators: === and !==, and their evil twins == and !=. The good ones work the way you would expect. If the two operands are of the same type and have the same value, then === produces true and !== produces false. The evil twins do the right thing when the operands are of the same type, but if they are of different types, they attempt to coerce the values. the rules by which they do that are complicated and unmemorable. These are some of the interesting cases:

'' == '0'           // false
0 == ''             // true
0 == '0'            // true

false == 'false'    // false
false == '0'        // true

false == undefined  // false
false == null       // false
null == undefined   // true

' \t\r\n ' == 0     // true

The lack of transitivity is alarming. My advice is to never use the evil twins. Instead, always use === and !==. All of the comparisons just shown produce false with the === operator.

Update:

A good point was brought up by @Casebash in the comments and in @Phillipe Laybaert's answer concerning objects. For objects, == and === act consistently with one another (except in a special case).

var a = [1,2,3];
var b = [1,2,3];

var c = { x: 1, y: 2 };
var d = { x: 1, y: 2 };

var e = "text";
var f = "te" + "xt";

a == b            // false
a === b           // false

c == d            // false
c === d           // false

e == f            // true
e === f           // true

The special case is when you compare a primitive with an object that evaluates to the same primitive, due to its toString or valueOf method. For example, consider the comparison of a string primitive with a string object created using the String constructor.

"abc" == new String("abc")    // true
"abc" === new String("abc")   // false

Here the == operator is checking the values of the two objects and returning true, but the === is seeing that they're not the same type and returning false. Which one is correct? That really depends on what you're trying to compare. My advice is to bypass the question entirely and just don't use the String constructor to create string objects from string literals.

Reference
http://www.ecma-international.org/ecma-262/5.1/#sec-11.9.3