The Filezilla client should be readily available in Mint's package management system. You can double check its availability with by opening up a terminal window and running:
apt-cache show filezilla
This should show you information about the package. To install, run:
sudo apt update
sudo apt install filezilla -y
Once you've installed it, just type it into the command line to run it, or go through your graphical "start" menu and find it there. Here's a visual guide for further reference. For general Filezilla usage, which should have the same UI regardless of the OS, see here.
You should be careful using the default ftp client since it offers no enccryption. Thus, passwords and other sensitive data you may transmit over FTP are easily sniffed. Thankfully, if you do want to go the command line route, you can use the sftp
client which has the same command syntax as ftp
.