I recently bought a 1990 Chrysler Dynasty, a week or so after buying it I noticed the spedometer wasn't working. It works sometimes pefectly, other days it goes from 0-180 in seconds (I wish my car was that good) and then back to zero and bounces around in the middle but it doesn't stay still, other days it simply doesn't work. I don't want to take it to a garage if it is going to be a lot to fix, I might as well get a new car, but if it's something relatively easy and cheap to fix I'd like to get it fixed. Any suggestions what could cause this?

Check the Variable Speed Sensor (VSS), located on the transmission. Remove and clean the connector. If the problem continues, replace the VSS. Should be an easy job.

That particular vehicle is prone to Vehicle Speed Sensor (VSS) failure.
When the speedo goes haywire, does the odometer still seem to function normally?
If not, you may need the VSS replaced. Chrysler/Dodge has a new sensor but it requires a modification to the harness that lead to it.
I would recommend having it diagnosed to verify what is causing the problem is before we speculate further, you know?