determining var type from prompt command and if else statement

= is assignment. == is comparison.

To convert the string that prompt gives you to a number, use parseInt(input,10) - that said, JavaScript will typecast for you, so there's no real need here. You can even tell if the user entered something that isn't a number by testing isNaN(input) for your "use numbers only" result.

So something like this:

var input = parseInt(prompt("How much is 2 + 2?",""),10);
if( input == 4) alert("Awesome!");
else if( input == 3 || input == 5) alert("Almost!");
else if( input == 10) alert("No GLaDOS, we're working in Base 10 here.");
else if( input == 42) alert("That may be the answer to Life, the Universe and Everything, but it's still wrong.");
else if( isNaN(input)) alert("Use numbers only please!");
else alert("You are wrong!");

I'd personally suggest:

var guess = parseInt(prompt('What is 2 + 2?'), 10);

switch (guess) {
    case 4:
        console.log('Well done!');
        break;
    case 3:
    case 5:
        console.log('Almost!');
        break;
    default:
        console.log('Seriously? No.');
        break;
}

JS Fiddle demo.

Or, to be more functional about it:

function answerMath (sum) {
    var actual = eval(sum),
        guess = parseInt(prompt('What is ' + sum + '?'),10);
    if (guess === actual) {
        console.log('Well done!');
    }
    else if (guess + 1 === actual || guess - 1 === actual) {
        console.log('Almost!');
    }
    else {
        console.log('Seriously? No.');
    }
}

answerMath ('2*3');

JS Fiddle demo.

Note that while eval() is the only means I could think of in this situation to evaluate the sum passed to the function as a string, I'm not entirely sure it's a good recommendation (albeit eval() has more bad press than it perhaps deserves, though it does present risks).

In most programming languages, = is assignment, and == tests for equality. So

a = 4 assigns the number 4 to the variable a. But a == 4 checks to see if a is equal to 4.

So for your code, you'd need:

var input = "" || 'number'
prompt ("How many is 2+2 ?", input)
if (input == 4)
  print ("Awesome !");
else if (input == 3 || input == 5)
  print ("Close !");
else if (input == 'number')
  print ("wrong number");
else if (input == 'random text')
  print ("use numbers only!")

I'm going to build on David Thomas's answer a little, because if you wanted to make it better, you could easily turn it into a little game.

var numa = Math.round(Math.random() * (100 - 1) + 1);
var numb = Math.round(Math.random() * (100 - 1) + 1);
var answer = numa + numb;
var guess = parseInt(prompt('What is ' + numa + ' + ' + numb + '?'), 10);

switch (guess) {
    case answer:
        alert('Well done!');
        break;
    case (answer - 1):
    case (answer + 1):
        alert('Almost!');
        break;
    default:
        alert('Seriously? No.');
        break;
}

Further things you could do would be to include a timer to see how long the user took to answer the question, and ask them if they way to play again when they get it right.

Here is a Fiddle: http://jsfiddle.net/6U6eN/