Simply open the catalog you have been using in Lightroom 3. Lightroom 4 will create a new copy of that catalog in the appropriate file format. Then you should just be able to continue working in Lightroom 4.
Thank you for your response, Jim. I am working from a laptop (I know, a cardinal sin!) and all of my work is cataloged on to several external drives. Given that LR doesn't allow any movement of files that aren't directly connected, how do I know that everything in LR has truly been transferred? What happens to all my edits if I were to uninstall LR3?
All of your edits are stored in the catalog. Your images are in the same state they were in when they were downloaded. If Lightroom 3 is finding everything on the different hard drives now, it should work just the same in Lightroom 4. Are you aware of the new process version in Lightroom 4 and how it will differ from what you have been using?
Regarding your edits, they are stored in the catalog. The updated catalog will contain all of your edits and will apply them to the images as they are displayed. Lightroom 3 and Lightroom 4 are completely independent. Once you are confident that Lightroom 4 is running satisfactorily you can uninstall Lightroom 3.