First of all, prepare for a slow download. According to numerous reports, macOS Big Sur downloads much slower than previous versions. This does not appear to be a bug, so there is nothing to fix. Just make sure you don't start updating in case you need your Mac ready to do something shortly.
What if the installation was successful but your Mac has been slow since then? The problem may be with older apps or too many apps running in the background. This is what you should do:
Disable login items. This is the first thing you should try, as too many apps opening at startup slows down your Mac. You can prevent apps from running in the background by going to System Preferences> Users and Groups> Startup Items. Just check the boxes next to the login items and hit the minus (-) button.