Look into sectors that interest you (e.g. energy, retail, charity). You can do this online, by attending employer events or by coming into our office to speak to a relevant employer in residence.
Learn about interesting organisations, visit their websites and investigate what roles they have available.
Let organisations know you're available
If, while researching, you find an organisation you'd like to work for but they don't seem to be advertising any jobs you can write to introduce yourself to them. Sometimes organisations will make room for people they think will be good for their team. As a general rule this approach works best with small and medium sized organisation in the private sector.
You will find help specifically on this on the Careers & Employability Moodle under "Online Training" (look for the course "Find Jobs & Internships" and the section "Go Pro(active) in 15 mins (3 of 4).