Fast locally, slow on my host

My <stack> site is quick on my machine and slow on <host>. The slow part:
<which pages or actions>

Help me find out why:
- How to measure where the time goes on the host, not locally.
- The usual differences: database on another server, no caching, a
  slower disk, a cold start, a small memory limit.
- Queries that are fast on a tiny local database and slow on real data.
- External calls my code makes that are slower from the host's network.

Tell me what to measure first and what each result would mean.