How can I replace Mavericks with an older OS without the use of Time Machine?

I updated without double checking that my time machine was turned on. It was off - I forget why (to save disk space maybe?)

My macbook is relatively old, but it was running fine until I installed Mavericks. Now it takes ages to get even simple tasks done.

Please help if you can! Is it possible to downgrade my OS to what it was before, but without the help of Time Machine data?