When needle felting the biggest risk is that of poking yourself with the needle, which since they are barbed can be especially uncomfortable. Make sure your needle tools are properly covered and/or that the plastic guards are properly locked when not in use.
While working with the needles the farther away you keep your free hand the better, a tool such as the Felting Claw and Mat Cleaner (#CFNC) allows you to hold down appliqué pieces and fiber while keeping your fingers well clear of the work. It is also important to have good work surface, the felting mats (#CFNM) and foam blocks (#CNFF) will allow you to felt projects without having to hold them in your hand. Remember, you want to stab the fiber, not you!
Needle Felting is also not a great project for small kids unless they are very closely supervised by an adult. However, it is a great way to work out some teenage aggression!
Wet felting can be a lot of fun, but it is very well, wet and wet can equal slippery floors. When doing wet or nuno felting make sure you have a waterproof floor or even set up your table outside on the grass if you have the option. If you can't be outside where the dirt will soak up your run-off water then make sure you have good shoes that will give you traction, and you may want to avoid working in an area that will get very slick, like on linoleum. It is handy to keep around a few old towels that just stay on the floor under your work table, then you can scoot them around as needed to sop up as you go. If you don't have a waterproof floor to work on, a plastic tarp layered over some no-skid rug mats works great too.
When you set up your work space make sure the table or counter you are going to be doing the rolling on is at a good level for you. Rolling felt is hard work and you don't want to throw your back out after only a few minutes. Good shoes, posture and surface height will make sure you can get through all the rolling and still get out of bed the next day.
Proper wet felting requires three elements, moisture, agitation and heat. Generally heat and moisture are supplied as hot water. Warm (about 105 degrees) is plenty hot enough to help open up the scales on the wool and facilitate proper felting. There is no need to boil yourself or the wool to get good results.
Staying aware and safe will ensure everyone has a good time.