The best and easiest thing to use is the jQuery Datatable plugin. Of course, at this very second, the website is down:
Edit: The site is back up now. Check it out for some really nice demos. The rest of my comment is below, as it still provides some good info.
To see what it's all about in the mean time, check out: http://www.codeproject.com/Articles/194916/Enhancing-HTML-tables-using-a-JQuery-DataTables-pl
There's also a working demo, with the search field in the upper right corner of the table, here:
That site above is actually for a plugin that adds a column filter as well, so you can search only a column. The default search for the Datatable plugin searches all fields in a row.