You don't need much in way of skills beyond the ability to hang on tight and be a strong swimmer. While riding the goal is just to hold on tight to the tube and have a great time as you ride on the water. Everyone who rides on the tube needs to be a strong swimmer, in case they let go and slip into the water, but otherwise pretty much everyone can ride on the inflatable.
In terms of things you need, the first thing you need is a boat to tow your tube.
You'll need a pump to blow the toy up with air. Some tubes come with these so check and see if yours does. A good pump can save you time and a lot of hassle, your tube should blow up in just a minute or two.
Anyone who plans on riding on the inflatable needs to wear a life vest. Falling into the water is a common occurrence. These water toys ride on the waves made by the boat, making for a strong current. Having a life vest will ensure that despite unseen factors (a particularly strong current, or a bump on the head) you are safe.
Consider wearing water helmets, especially when you have multiple riders. This is because it's so easy for two riders to bump heads (or hit something like a log or other unexpected debris in the water) and then fall in. If you're unconscious, or confused, even briefly this can be extremely dangerous. To avoid this situation consider getting water helmets, they'll protect your head and help ensure your safety.
Make sure you have a good tow rope or harness that doesn't have any frays or tears. These can become a safety issue, so it really is important that you have a sturdy rope to use to attach the tube to your boat.
And of course, the fun part--you need riders!