How can I determine if a variable is 'undefined' or 'null'?

You can use the qualities of the abstract equality operator to do this:

if (variable == null){    // your code here.}

Because null == undefined is true, the above code will catch both null and undefined.

The standard way to catch null and undefined simultaneously is this:

if (variable == null) {     // do something }

--which is 100% equivalent to the more explicit but less concise:

if (variable === undefined || variable === null) {     // do something }

When writing professional JS, it's taken for granted that type equality and the behavior of == vs === is understood. Therefore we use == and only compare to null.

Edit again

The comments suggesting the use of typeof are simply wrong. Yes, my solution above will cause a ReferenceError if the variable doesn't exist. This is a good thing. This ReferenceError is desirable: it will help you find your mistakes and fix them before you ship your code, just like compiler errors would in other languages. Use try/catch if you are working with the input you don't have control over.

You should not have any references to undeclared variables in your code.

Combining the above answers, it seems the most complete answer would be:

if( typeof variable === 'undefined' || variable === null ){    // Do stuff}

This should work for any variable that is either undeclared or declared and explicitly set to null or undefined. The boolean expression should evaluate to false for any declared variable that has an actual non-null value.