I host my websites on a VPS as well. It's absolutely worth the extra effort (so much more flexibility), but the setup does take a little longer and there are a lot of things that need to be configured. There could be any number of reasons for your performance issues.
Just out of curiousity, how large is your forum? What host are you using (and what plan, as in RAM and CPU does it have), and what does "top" or "htop" output for server load in the command line? Look for the "server load" line that will look something like this:
1.33 0.99 1.5
Those numbers represent, on average, how many cores the server is trying to use over the last 1 minute, 5 minutes, and 15 minutes. For example, if you have a dual-core VPS, you never want those numbers to exceed 2.0. If you're seeing very high numbers, it indicates your VPS is heavily overloaded. This does not necessarily mean it's your fault. Sometimes neighboring VPSs aren't behaving and they cause your load numbers to shoot up, so it just depends. Are your performance issues intermittant? Do they come and go or is it pretty much consistently slow?
My guess is that MySQL likely isn't the culprit unless you're running a large forum (the defaults are usually sufficient for small to medium forums). I'm curious as to whether the server is having IO thrashing or if it has run out of RAM. It could also be a configuration issue with Apache and PHP (try using php-fpm, it's much easier on RAM).
If you're running a larger/busier board or if MySQL is the culprit, I've found this guide
to be extremely helpful for performance-tuning MySQL (I use this on every server I set up). Pay very special attention to the caches (both for MyISAM and InnoDB). Those control how much data MySQL stores in RAM. Larger databases require much more cache in order to avoid slow queries. (It's generally good practice to dedicate about 50% of your server's RAM to MySQL in most cases).
In any case, it's not something that can't be fixed. Could be any number of things, but we will narrow it down and find the culprit.