How can I speed up my old Mac mini?

What year model Mac mini?

see > Identify your Mac mini model - Apple Support

Some Mac mini models have user upgradable RAM and some do not.

see > Upgrade or install memory in your Mac mini - Apple Support

In addition, upgrading RAM will only allow you to open and run more App’s at the same time. It will not speed up a Mac mini with a slow, full or failing Hard Drive.

Before doing anything else, get and run EtreCheckPro,

from > https://etrecheck.com/en/index.html

Then post back here with your EtreCheckPro report,

as per > How to use the Add Text Feature When Post… - Apple Community

If it still uses HDD, replace it with SATA SSD.