Which are the most effective methods of optimizing a drupal 7 site?
Boost module is the best option for performance issues, even it will works great in shared hosting. It will not hit the server for every request, instead it cache the pages and deliver them and Boost will cache &amp; gzip compress html, xml, ajax, css, &amp; javascript. Boosts cache expiration logic is very advanced; it's fairly simple to have different cache lifetimes for different parts of your site. 


  Boost provides static page caching for Drupal enabling a very
  significant performance and scalability boost for sites that receive
  mostly anonymous traffic. For shared hosting this is your best option
  in terms of improving performance.