hi sionicle and welcome to the UU forums!!!
tough questions as there is a lot involved...
For me, the simplest way to learn to strum is to pick a song you know really well...then get the sheet music for it...it's probably easiest to start strumming by using your index finger, relax your wrist and let your strumming hand move across the strings in time with the natural rhythm of the song...when you do that, a natural strum pattern will start to take shape that you'll feel inherently comfortable with....the more you practice, the easier it'll get
with the Jason Mraz song it's a little more complicated as you'll need to develop a strumming skill called "chunking" or "palming" where you mute the strings by pressing down the heel of your palm over the strings at either the bottom or top of the strum
To learn about some basic strum techniques you can trawl through Aldrine's videos on this web site, also look on previous threads on this "Beginners" board where there are a number of threads about strumming, and chunking.
Also, there is a great DVD available by a guy called Ralph Shaw called "Essential Strums for the Ukulele" which is really, really good
All the best with it mate...like anything, practice will get you there, just keep persisting and your time spent will ultimately pay off!!!