It completely depends upon what you are upgrading as to what you should do (i.e. is it a mission critical site or your personal blog etc).
How bad is it if things go a little pear shaped?
You should also decide which branch to install - currently there is 1.x and 2.x.
One main difference between the two is that 2.x drops support for IE 6,7,8
Also, here is a good article on some of the new 2.x features: http://www.sitepoint.com/whats-new-in-jquery-2-0/
Hope that helps.
Let us know if you run into any difficulties.