There are many views on the “correct” way to hold a ukulele. Some people say it should be tucked under your arm, others have it resting on their lap whilst some players prefer to use a strap. The important thing is that you must feel comfortable holding it, so after some experimentation you’ll find which way suits you best.
For right-handed people the most common way is to rest the neck of the ukulele in your left hand in the crook between your thumb and index finger. This means that your right hand is free to strum the strings. In the photo above, I’m holding my Laka Joe Brown signature soprano ukulele under my arm. As it’s a small instrument I find it comfortable to tuck its body underneath my right forearm, squeezing it gently to hold it in place. For the larger tenor ukuleles I tend to use a strap which supports the instrument and frees up my strumming and fretting hands. Most players like to play their instruments whilst sitting down; however if one finds oneself having to play whilst standing up, at a concert for example, then a strap to support the ukulele would be very useful.