Same way you solve it on any other computer.
Figure out what is causing it and go from there.
Standard one is see what is running and see what is going.
Mint will include a task manager, though you can also use the "top" command in a terminal to get one. I don't know what we are suggesting for hard drive load these days and what mint has (iostat, iotop or just continually reading the sda or whatever part).
If said program is gobbling all the memory or CPU then figure out why that might be (plugins, bugs*, and then either take steps to negate it or add more memory/CPU (or speed up what there is).
*skype here for instance always uses a full core when I stop a call. Have to close it down and load it back up.
Depending upon what you are doing then "swappiness" is a command you might want to look at. This will change what Linux does as far as using swap (a portion of the hard drive it sets aside to use) vs normal memory.
For individual programs there is also the niceness vs priority
https://askubuntu.com/questions/656771/process-niceness-vs-priority
Linux does not always prioritise the same things as other operating systems. Some choose to assign priority to the UI so even if the program hangs the UI will still respond which might be what you are seeing.
If it is a full lock up you have seen do remember ctrl, alt and usually F1 through F8 will give you other terminals you can log into and that usually survives the UI crashing or locking.
Is your hard drive OK? A dying hard drive can tank performance.
Likewise is your CPU fan clear? My laptop slowed right down a while back and after I took out about half a hamster of dust it was lovely again. The fan going all the time might be a sign of this.
You can also select CPU priorities
It might well be that the drivers available for your particular flavour of laptop don't work well with mint of the present day.
What desktop environment are you using? Some of the full fat mate and cinnamon stuff is a bit slower than the likes of XFCE (or even more cut down things like LXDE). All should be easy enough to install and select from (usually when you are logging in as a user from a GUI).
This can go on for a while and it is fairly standard between operating systems, though might go under different names.