1. How big and how full is your system drive? In Finder, select your drive and run "File→Get Info". Capacity and Available space are listed in the "General" section at the top of the Info window.
2. How big is your Aperture Library? In Finder, select your Library file and run "File→Get Info". The size will be reported at the top right of the Info window. You may have to wait a couple of minutes for Finder to calculate the size.
3. Are your Images' Masters Managed or Referenced (or a mix)? Referenced Masters are badged (you can show Badges on any of the seven Metadata Overlays, as well as on the Metadata tab of the Inspector). If any are Referenced, determine where they are stored, find them, and find out how much storage space they occupy.
In general you should keep at least 15% of your system drive free (empty) in order to not crimp your system's performance. It is normal for Aperture users to run out of storage space on their system drives. The common solution to convert some or all of your Images' Masters from Managed (= stored inside the Aperture Library) to Referenced (= stored outside the Aperture Library, usually on a different drive). Aperture provides tools to move your Masters wherever you would like them. NB: Referenced Masters are not backed up by Aperture's Vault feature, and are not backed up automatically when you back up your Library. Therefore you must add to your backup protocol something that includes backing up your Referenced Masters.
There are many many reasons for slowing performance. Lack of free space on your system drive is a common one, but you should not rule out others without checking. It is also advised to run Software Update to make sure your OS and other programs are completely up-to-date.
Good Luck.
