How to get, set and select elements with data attributes?

To reflect the values of the Attributes immediately in the DOM you can use .attr()

$('#element').attr('data-data1', '1');  // Sets the attribute

$('#element[data-data1="1"]') // Selects the element with data-data1 attribute'

$('#element').data('data1'); // Gets the value  of the attribute

$('#element').attr('data-data1'); // Gets the value  of the attribute

In plain Javascript you can try this

var elem = document.getElementById('element');

elem.setAttribute('data-data1', '1'); // Set the attribute

elem.getAttribute('data-data1'); // Gets the attribute

All of the answers are correct, but I want to state something that nobody else did.
The jQuery data method acts like a getter for html5 data attributes, but the setter does not alter the data-* attribute.
So, If you manually added the data (as is stated in your comment), then you can use a css attribute selector to select your element :

$('#element[data-data1=1]')  

but if you have added (altered) the data via jQuery, then the above solution won't work.
Here's an example of this failure :

var div = $('<div />').data('key','value');
alert(div.data('key') == div.attr('data-key'));// it will be false  

So the workaround is to filter the collection by checking the jQuery data value to match the desired one :

// replace key & value with own strings
$('selector').filter(function(i, el){
    return $(this).data('key') == 'value';
});

So, in order to overcome these issues, you need to use the html5 dataset attributes (via jQuery's attr methos) as getters and setters :

$('selector').attr('data-' + key, value);

or you can use a custom expression that filters jQuery internal data :

$.expr[':'].data = function(elem, index, m) {
    // Remove ":data(" and the trailing ")" from the match, as these parts aren't needed:
    m[0] = m[0].replace(/:data\(|\)$/g, '');
    var regex = new RegExp('([\'"]?)((?:\\\\\\1|.)+?)\\1(,|$)', 'g'),
    // Retrieve data key:
    key = regex.exec( m[0] )[2],
    // Retrieve data value to test against:
    val = regex.exec( m[0] );
    if (val) {
        val = val[2];
    }
    // If a value was passed then we test for it, otherwise we test that the value evaluates to true:
    return val ? $(elem).data(key) == val : !!$(elem).data(key);
};

and use it like :

$('selector:data(key,value)')

Update

I know this thread is a few years old, but since it has some activity, it's worth mentioning that doing this using the querySelector dom API (with no need for jQuery) is quite trivial:

document.querySelectorAll('[attribute=value]')

// Set
$('#element').attr('data-value', 'value');
// Get
var value = $('#element').attr('data-value');
// Select
var elem = $('#element[data-value = "' +value+ '"]');