As suggested, 1 GB RAM is really almost the basic suggested minimum for running Leopard 10.5.x and the absolute minimum just for a basic SL 10.6.x install.
In the interim, try shutting down your Mac, wait 30 seconds of so and boot up using Safe Boot Mode by holding down the shift key until you see the spinning gear wheel.
Then run Disk Utility and repair permissions and verify disk.
If you get pages and pages of repair permissions, do the repair permissions maybe at leat two or thre moormr time.
It may take a while depending on various stuff, and then finally just restart normally and see if things have improved.
Then order and get at least 4GB RAM installed, but that Mac can use 6 GB RAM if you want.
For full specs see: Lookup Mac Specs By Serial Number, Order, Model & EMC Number, Model ID @ EveryMac.com
Edit: check out the canadaram site and check his note:
"Macintosh intel MacBook Core2Duo 1.83, 2.0 and 2.16 GHz - MacBook2,1 black and white
Two sockets, can take 1 x 1 Gb + 1 x 2 Gb for 3 Gb total. With 2 x 2 Gb, 3.0 Gb is usable by the OS but you get Dual Channel memory access for a 6% - 8% speed improvement"
Canada RAM sells memory in Canada - Apple MacBook Intel CoreDuo and Core2Duo SantaRosa and Penryn