Most people find that, after a bit of practice, it's not too hard to hold a ukulele. However, some people prefer the security of a strap, particularly if they are playing something intricate.
Since most ukuleles do not have pegs for straps, you can use what is known as a 'ukulele thong'. This goes round your neck, under the ukulele and hooks on to the soundhole.
James Hill often uses a guitar strap going over the shoulder. This method is more sturdy but means you'll have to put strap pegs on your ukulele.