I have a HTML table with a column that contains a button at the end of each row:

echo "<td><button type='button' class='btn btn-primary'>View Order </button></td>";

How can I make this button link to viewOrder.php and also pass the order number from the first column on the same row for e.g. viewOrder.php?id=<data from column 1 here>.

echo "<td><button type='button' class='btn btn-primary' onClick='window.location.href='viewOrder.php?id='+orderNumber'>View Order </button></td>";

Unable to provide more, as need more code.
If your order number is some div or span, etc that have id="orderNumer", use document.getElementById("orderNumber").innerHTML.

Assuming you have a PHP variable $orderNumber:

echo "<td><button type='button' class='btn btn-primary' onClick='doThing({$orderNumber});'>View Order </button></td>";

Now you need to define the method doThing in javascript:

function doThing(ordernum)
{
    document.location.href = "viewOrder.php?id=" + ordernum;
}

Since your button is taking you to a new page, and you are asking for a get request, I think you should use a link. Optionally you could style the link to make it look like a button.

This way you avoid the use of java-script to do the get Request by appending the orderNumber in the URL.

Since it seems you are using BootStrap, you can use the btn btn-primary classes to make the link look like a button

Try this:

echo "<td><a href="viewOrder.php?id=$ordernumber" class="btn btn-primary">View Order</a></td>";

JSFiddle