A very obvious question asked by ukulele beginners is how to hold and strum the thing!
As with most things musical instrument related, you will find a lot of resources out there that tell you that you MUST do this or that. Usually they are wrong, and miss the important point of doing what you are happy and comfortable with. Look at it this way - did Jimi Hendrix play his guitar in the same way as a spanish flamenco player? No. They are both guitars, but they have different styles. It's the same with ukes. Don't get too hung up on rules, but do bear in mind that certain styles will make your playing and development a touch easier.
HOLDING THE UKE
The ukulele is designed to be held by the strumming arm against the body. They are not particularly heavy, and by placing the uke against the chest you should find that you are able to hold the uke against you by pressing the the top of the uke below the soundhole against your chest with the inside of your bicep.
But as I say, that is not a hard and fast rule. Some people prefer to play sitting down and rest the uke on their knee - thats good too. If you want to stand but struggle with holding the uke, you can resort to a full strap or support like the UKE LEASH
This video may help you on this topic
Do what feels right to you!
STRUMMING THE UKE
The conventional method for strumming the ukulele is to use the fingers of the strumming hand. The traditional style is to only move the wrist keeping the forearm fixed (and holding the uke). You ideally need to strum over what we call the "sweet spot" which is usually at the end of the fingerboard in front of the sound hole (note - this is the opposite of the sweet spot for an acoustic guitar which is normally strummed behind the soundhole)
But again, that is not a hard and fast rule. I have what you may call an unusual uke strumming style (check out my videos) as I tend to rest the fleshy part of the side of my hand (thumb side) just above the sound hole, and strum with my forefinger downwards. I can strum in the conventional way, but I just find this more comfortable to me.
Some folks will rely just on their thumb to strum ( a very laid back style) or use a pick. Again its all good.
If you are starting out, you will read lots about strum styles and patterns, fans and triplets. Honestly, this is more advanced stuff than you need right now - just concentrate on getting the ukulele in a position you like, and a strum that you can do effortlessly and in good rhythm before worrying about fancy strum patterns. Seriously, I have seen so many beginners who can copy a complex strum pattern by heart but have absolutely no sense of basic timing. I really think those people have learned things completely the wrong way around!
Youtube is your best resource for seeing people play - do a search for ukulele and have a look at the many different ways people hold and strum the uke.
Find what works for you!