Linux/Unix systems administration is my bread and butter. At my previous job (of 10 years) one of the things I managed were some MySQL database servers that were the backends for multiple web sites and these needed constant tuning due to poorly constructed queries, missing indexes and then MySQL itself has a shed load of settings that need to be set correctly.
The main thing with Apache is that you need to make sure it can handle the number of connections that are attempting to be made.
Overall the process involves looking at memory, cpu, disk io usages.
Checking the Apache configuration.
Looking for slow MySQL queries, analysing the queries that are being used, look for missing indexes and optimise its configuration. Sometimes a restructure of the database is required.
Check the kernel configuration in areas of memory management, cpu and IO scheduling and networking.
You don't mention what OS this is on, so I'm going to assume Linux. Might be worth adding that to the description.
Feel free to contact me if you have any questions.
Cheers,
Andrew