It all starts with your content. What are people trying to find when they come to your site?
Beware of site ROT (redundant, out-of-date and trivial). The best thing you can do to create quality content is to clean up the old, out-dated, or irrelevant content across your site. Remember that people don't read; they scan. Remove flowery, or decorative text and keep it simple. Smashing Magazine published a nice article about managing ROT.
Take an inventory of the content of your site, and compare it with your Google Analytics data if possible. Weed out old pages that see very little traffic, and rewrite content as needed. Keep in mind that your website is not a historical account of everything you've done since it was launched. Download a copy for your department records if needed, but websites are not storage.
Remember to think like a user. As an academic institution, we have a diverse audience, but students are often at the heart of it. Watch out for jargon and acronyms that a first-time visitor to your site isn't likely to understand. For example, we might know that CMS stands for "Content Management System", but we only know that through context and exposure.
Need more guidance? Content Strategist, Hilary Marsh has tips to Declutter Your Website (Video).
Know your content. Your website should be the source of information that only you can provide. Convey that knowledge in a professional and concise manner, so users will see you a reputable source for information.
Keep your site up-to-date. An easy way to do this is to leverage tools like our Events Plugin or Tiles. By introducing well-written content in regular intervals, you keep the site from becoming stale, and users respond by returning to your site for information.
Publish "teasers" on your social networks, and make it social. Good header text and a crisp image can go a long way to draw traffic to your site. If your content would make a nice Tile, you can submit it to email@example.com to be featured on the UM homepage.