The easiest might be to contact your host. They can probably give you the info on if you have SSH access, or if it's a Windows server, then if you have Remote Desktop access.
I'm going to guess they probably just set you up with the standard MySQL configuration. But the main thing will be to get some kind of idea on what the processing time looks like during a slowdown period. Maybe start a topic on your site and when any of your users experiences a slowdown, have them paste the bottom debug line that shows the page generation time into that thread so we can get some data.
