You can do it a bit more often that twice a day, I'd say at least 5 times a day. Of course starting out, if your pets are very uncooperative, twice a day is good for the first day or two.
I actually use a variety of techniques with my pets. Chinchilla like to have their back feet supported when possible. Using the base of the tail can be very helpful when trying to position your pet. It is a very sturdy way to restrain a pet that is combative. If you dangle your pet by its tail, just for a split second, it can buy you time to get a better hold. I know it looks really bad to do that but the way chinchillas are built you'll discover it actually causes them less stress than grabbing them under the arms which is also a good technique. Once your chin is tame that will be the normal way to hold it, one hand under the back feet, and the other around the chest. I don't make a habit of lifting them by their tail but consider it a usable technique to use when handling and certainly something to try out. My pets are tame enough to be lifted with one hand but do not try that with just any chinchilla because if they fall onto those hard shelves they can be seriously injured.
Avoid putting a lot pressure around their middle where their organs are and be very careful not to snag their feet which can cause some real damage. Keep in mind your pet will want to lunge forward so putting your hand in front of their head can help control this. Do not let them flail around in your hands. If they are flailing around and you don't have control let go immediately. To prevent this make sure you only pick up your pet when it is in an easily accessible part of the cage.
When reaching into the cage try not to approach them from directly above or chase them in the cage if you can help it and this will make your pets more comfortable. Try to predict how they are going to land when you let them go to make sure they will not fall or ram into something that can injure them.
My chinchillas are typically inactive during the day and much more awake after sundown. I recommend initially handling them during their inactive times and they'll be a little slower. If you do manage to drop one or have a chin get away I've found it helpful to have a rod of some kind like a broom handle to chase them out from under furniture. I use a plastic grabber with tongs on it (don't use the tongs part!) that's safe to push them around with. In my situation I can close the doors in my hallway and chase my pet out of my room and into the bathroom where there is nothing to hide under. Try to minimize stress by making the chase as short as possible. My oldest chinchilla has a habit of jumping away from me when I sit with him at my desk and catching him is very difficult. Most are. Some owners give their chins the run of the room which makes them less likely to run away. I don't recommend that because they tend to chew power cables and don't usually survive when that happens. And that is only one potential hazard to consider.
So there's a lot to consider. In practice it's really not that terrible. Think ahead of your pets and it should go smoothly.
