Mendeley is a fantastic piece of software designed to make referencing things much easier. To get it working at uni, download the portable version from my homepage.
When Mendeley starts on a new computer it will ask you to sign in. Because all your preferences are saved to the C: drive it's worth sticking to a single computer when you are working.
Once the main program starts (and you have logged in to retrieve your cloud-synced files) it will be worth modifying some settings in Tools/Options. The one's I'd recommend are shown below; let Mendeley rename your papers and sort them into a folder with the rest of your project. Remember this option will need modifying each time you change computers.
You should also go to Tools and click Install MS Word Plugin, now when you're in Word just press Alt-M and insert a reference! You can even download the official Leeds referencing style by going to View > Citation Style > More Styles... > Get More Styles and search for Leeds. You can see it being used below:
To add papers to Mendeley, simple drag them into the window. It will then search Google for related metadata and automatically populate the details tab. It's worth checking this before you OK it. You can also add manual entries (ie for books) from the File menu.
To read a paper, simply double click it. You can then highlight key passages and those highlights will sync to your other Mendeley installations. You can also attach notes for yourself.