I'm new to all this stuff so be gentle :)

If you remove that bullseye from your forehead, I won't shoot.

Does anyone have any ideas where to look or which logs/performance stats to check?

Yeah, first look at your code. How much data are you retrieving? How do you process it? (one record at a time, or all records at once) Caching any of it? (can you make use of caching) Check your error logs for errors, check your mysql logs for errors, try profiling your code, try profiling your mysql.