Your first step is to look at a few simple tools that could give you ways to get perceived (and actual) speed-ups. These are your low hanging fruit, before spending time (and money) on infrastructure upgrades.

Look for a 'YSlow' plugin for your chosen browser (they exist for Chrome and Firefox), which can help you to identify things that are causing your site to appear slow.

After that, then I would look at CDN, and then I would look at database optimisation (many people just don't "get" indexes, and don't understand how much of a difference they can make), and finally code optimisation.