Most distributions have detailed instructions on their sites, like Linux Mint. But overall, it amounts to:

1. Choose disteibution
2. Download it's installation image ( I recommend LiveUSB version - it will allow you to check if you like it first and most distributions have them )
3. Prepare bootable usb stick ( I recommend Rufus for that )
4. When done, reboot your computer choosing usb drive as boot
5. If LiveUSB version, check out whether you like what you see and if everything works. If you like it, there should be install app on desktop
6. Proceed with install process. For most linuxes, it's 1:1 windows installation process, minus ads and forcing you into online stuff.
7. Enjoy linux ^^

Edit: Also, you can simply download distributions en masse and boot them up in VirtualBox or something to check them out without making USB each time. Allows bypassing requirement of LiveUSB too - you can just install it in its box. However not all distributions like being virtual boxxed