Every fast website relies on caching. The idea is simple: keep a copy of something expensive so the next request gets it instantly.
Browsers cache images and scripts. CDNs cache whole pages close to your visitors. Databases cache frequent queries in memory.
The hard part is knowing when a copy is stale. Set clear expiry times, and clear the cache when the data changes.
Start with your slowest page. Caching it is often the biggest speed win you will get.