A few tips:
"Inspiration is about framing a design challenge and discovering new perspectives on the opportunity."
- IDEO, Design Thinking for Libraries
"Try this: walk around your library and ask yourself why things are the way they are. Why is the circulation desk set up the way it is? Why is the reference collection where it is? Why are the recycling bins where they are? We bet that the answer to most of the questions you ask yourself will be, 'Because that's the way it's evolved.'"
- Aaron Schmidt and Amanda Etches in Useful, Usable, Desirable
Look with fresh eyes. Pretend you are a patron walking into the library or visiting the website for the first time. How does the environment help or hinder you in getting where you want to go?
Are you ready to make intentional design decisions in your library, instead of just doing things the way they've "always been done?" Great! Start by defining a goal (or if you prefer, a "design challenge.") This can be something as big as renovating your building or as small as improving a display of your upcoming events.