Assuming that what you want is to iterate through each exercise, display something static and wait for the timeout to expire before moving on to the next, I might do it like this:

<h1 id="exercisename">Get Ready</h1>
<p>Click the button to start the exercises.</p>
<button onclick="nextExercise()">Begin</button>  
<script>
var exercises = [
    {
        "desc":       "Pushup/Pullup",
        "countdown":  3
    }, {
        "desc":       "Squat punch",
        "countdown":  4
    }, {
        "desc":       "Jumping jacks",
        "countdown":  6
    }
];
var excount = 0;
function nextExercise()
{
    var ex = exercises[excount++];
    var name = document.getElementById('exercisename');
    if (typeof ex == 'undefined') {
        name.textContent = "Done";
        excount = 0;
    } else {
        name.textContent = ex.desc+" for "+ex.countdown+" seconds";
        setTimeout(nextExercise,ex.countdown*1000);
    }
}
</script>

Obviously for a real workout, you'd probably want to increase the times a bit. :)

Assuming that what you want is to iterate through each exercise, display something static and wait for the timeout to expire before moving on to the next, I might do it like this:

<h1 id="exercisename">Get Ready</h1>
<h2 id="seconds">0</h2>
<p>Click the button to start the exercises.</p>
<button onclick="nextExercise()">Begin</button>  
<script>
var exercises = [
    {
        "desc":       "Pushup/Pullup",
        "countdown":  3
    }, {
        "desc":       "Squat punch",
        "countdown":  4
    }, {
        "desc":       "Jumping jacks",
        "countdown":  6
    }
];
var excount = 0;
var timeleft = 0;
var secondsTimer;
function setSeconds(s)
{
    var sec = document.getElementById('seconds');
    sec.textContent = timeleft;
}
function tick()
{
    setSeconds(timeleft--);
    if (timeleft <= 0){
        clearInterval(secondsTimer);
    }
}
function nextExercise()
{
    var ex = exercises[excount++];
    var name = document.getElementById('exercisename');
    if (typeof ex == 'undefined') {
        name.textContent = "Done";
        excount = 0;
    } else {
        name.textContent = ex.desc+" for "+ex.countdown+" seconds";
        timeleft = ex.countdown;
        setSeconds(timeleft);
        secondsTimer = setInterval(tick, 1000);
        setTimeout(nextExercise,ex.countdown*1000);
    }
}
</script>

Obviously for a real workout, you'd probably want to increase the times a bit. :)

Update:

Based on a comment, I've also added a countdown timer. Note that the countdown is handled as using setInterval while the exercise timers use a separate and independent setTimeout.