Okay so you can either do this through ajax or through a page reload, a page reload is going to be much easier, but you can get it to work without reloading the page...
Reloading the page
You can basically make it so that when a user selects an option, use jQuery to redirect to the current page and append the <option>
value to append as a query string, so your template could look like this:
<select id="sortQuery">
<option value="postDate asc">New - Old</option>
<option value="postDate desc">Old - New</option>
<option value="title asc">A-Z</option>
<option value="title desc">Z-A</option>
</select>
Then, you can do this in your template:
{% set orderJs %}
$(function(){
$('#sortQuery').on("change", function(e){
// Get the value from the select
var filter = $(this).val();
// We can use twig because we are setting this in template, if you extracted this to its own file, you would need a different means to output the page url
document.location.href = '{{ craft.request.getUrl() }}?order=' + filter;
});
});
{% endset %}
{# let craft include the script to the end of our template #}
{% includeJs orderJs %}
Then, in your template file your code could be:
{% set counter = 0 %}
{# Either get the order from the query or use a default #}
{% set order = craft.request.getParam('order', 'title asc') %}
{% for entry in craft.entries.section('tips').order(order) %}
{% set counter = counter + 1 %}
{% include 'includes/tip-blocks' %}
{% endfor %}
This should then reload the request with the query string, craft will see it and update the response accordingly. I must stress this is untested, but it should work...
Without reloading the page
This gets a little more complex and would involve more jQuery/Javascript than craft so I won't go into too much detail about it.
The steps are pretty much the same as above, except within the script tags (where you listen for a select change) you would make an ajax request to either a html template (which contains the sorted results) or even using the ElementApi plugin to return json (from a template) which you can then iterate over in jQuery and then update your DOM accordingly.
I hope this helps get you on track!