There's a few tools you can use to gauge performance, or check resource usage. If you're using the defaults for MySQL though, chances are, that's one issue that's leading to the spikes. The defaults for MySQL aren't meant for production use and aren't really optimized for more than light traffic.
apt-get -y install htop
htop will provide a more detailed look with better sorting than standard
top. You can hit
F6 to sort by CPU, MEM, etc. You can also use F6 to expand the process tree and view child processes.
apt-get -y install mytop
mytop will give you information about threads, queries, key performance, etc in real time.
MySQL Tuner isn't a monitoring agent, so to speak, as much as it is a tool to gauge performance and help optimize your configuration. It'll make suggestions on how you can improve performance, as well as detail how your current configuration is working for you. Its very detailed.
The one thing to note about MySQL Tuner is that MySQL needs to be running for at least 24 hours before each run so that it can gather proper stats. So if you run MySQL Tuner, and then make a few changes, unless those changes cause larger issues than you're already having, you need to give it a bit of time before running it again.
mysql -u root -e 'show processlist'
You can also just run this command from the CLI, though
mytop would be a better option since it's continuous and live, whereas this is a one-off command.