Install APC and Memcache and their extensions
If your stuck with shared hosting there are a couple of options to make Drupal faster.

Use some form of a file cache for the page cache. Boost &amp; filecache's filecache_fast_pagecache option will serve cached pages a lot quicker than core does. For the other cache tables filecache or Drupal's core database cache might be quicker; you'll have to test to see what one works better on your shared hosting.
https://drupal.org/project/boost
https://drupal.org/project/filecache

Optimize your database. This is a post of things that can be done on the drupal side; there is a lot more that can be done if you can change the mysql side.
Drupal 7: Database select query FROM cache_bootstrap brings server down