There's not much it if your chinchilla likes the critical care solution and will eat it off the top of the syringe which is sometimes the case. Worst case is your pet will fight you. In that case I recommend feeding having one person hold him and the other person with the syringe. Get the tip behind the front incisors. There is a gap there. Don't aim the syringe down the throat because if you manage to squirt it down the throat you can cause choking or aspiration of fluid into the lungs.
With one person it's a little harder. Sometimes you can wrap them in a towel and that can help restrain their legs. Always have everything ready to go in advance so the process goes very quickly once your pet is out of the cage. Usually, if you're doing what you are supposed to do and keeping track of their food intake and fecal output each day, you'll know when your chinchilla is getting sick and you'll probably end up with a vet visit before it gets that bad. The vet can show you as well especially if he prescribes antibiotics for any reason that can cause anorexia.
