You can search for "filezilla" or jump straight to the download page. Click on the link for the latest release (not beta version) of the client. This will take you to the page where you will have the option of downloading the source or object program in compressed or uncompressed files. You want the object program, so the simplest thing to do is download the automatic installer "FileZilla<current version>setup.exe". (For example FileZilla_2_2_32_setup.exe).
Follow the wizard instructions to complete the install.
You will not be able to install FileZilla in the labs on campus, but you can still use it from those machines by installing it on a flash drive.
There are several Web sites with libraries of applications you can install on a flash drive. One is: http://portableapps.com/, where you will find Filezilla and several other useful tools like Notepad++, a text editor, the Firefox Web client and GIMP, an image processing program.
The FileZilla download page includes links to documentation and support forums. You can install the version of Filezilla you find there on a flash drive, and use it in the school labs.
You can display and edit files from within FileZilla if you select a text editing program to use. You do that by selecting the Edit>Settings menu and clicking on File viewing/editing. You then browse to the executable (.exe) file for the text editor you want FileZilla to invoke. For example, if you want to use Microsoft's Notepad editor, it usually is at c:\windows\system32\notepad.exe on a Windows XP computer.