Jenkins has very quick release cycles, and statistics shows that there is a release for every 6.59 days. The release process page will state that an RC freeze is schedules for Monday, and then late Friday the RC is released. Also, there is a Long-term Support version available that is put together every 3 months and is suitable for more stable installations.
The upgrade process itself is super easy. It does not matter if you are using Linux, Mac OS or Windows; there is a single, easy way for upgrades built into the product itself.