Learning To Play The Ukulele: Tips and Resources

Learning to play is repetition and practice. You can play it sitting down, but learning to play standing up can help you later on when when you a good enough to play with others, in a group or in front of others. It fosters good posture and habits. Of course you can sit down, but try to stand up when you practice as well, so you will be comfortable with it later on.
Practic your chords, running through the progressions, over and over so you can easily switch between them easily.  I recommend a basic learning book that is spriral bound, so that the pages will stay in place after you turn them.  If you are playing along with a video, try doing it standing up, and eventually your body will begin to feel the music more, so that it's not just a thinking excercise, but so you begin to relax and feel the music and timing as well.  When you can play the chords comfortably, pick out a simple tune and sing along while you are strumming.  Don't worry about your voice, if you don't feel you have a good one.  Singing along, or humming the lyrics will help your playing and make it more enjoyable, and in time, you actually will improve your singing ability.
You can find free tabbed music with some simple searches on the internet.  I find that watching video lessons is very helpful as well, and I put the links to my favorites for you to try out below.  I would watch each all the way through first, then grab your uke and follow along, with your finger ready to pause or go back when you need to.  Have fun!