My system is considerably slow and I have no idea why and no idea what information I can provide to help determine the cause. What basic trouble shooting can I do to obtain and provide useful information about what the problem might be?
There are commands that you can issue and edit into your post that will be useful in helping you determine what your problem is. As Rinzwind suggests here
top -o %CPU | head -n12
could be useful. Also
grep -i error /var/log/syslog and
dmesg can provide useful output. A failing hard drive can also have a major impact on system speed especially in situations where files are being processed or swapping is taking place. It's a good idea to check the SMART status of your storage devices on occasion. Another possibility is failing to meet the minimum requirements of the version of Ubuntu you have installed as alluded to in this comment by pa4080.
If the problem is slow booting,
systemd-analyze blame can also provide useful information.