This answer assumes lifting aids are being used for general training. Not for physical therapy or rehab.
In a general, it's actually very opinionated. There's no actual right answer as to when to start using lifting aids. Though there are a few guidelines that most people follow.
First, there's no real reason to use gear for anything other than lifts like squat, bench, deadlift, clean, snatch, arguably overhead press, and any variation of those. Those movements are for strength training and they're full body so you tend to lift heavier and exhaust easier.
There's a massive write-up by Greg Knuckols about belts. The TL:DR version is that belts have been shown to increase performance in the gym when performing the big lifts. He argues that the increase in performance leads to increase in volume which leads to bigger gains in the long run. As such, it is to your advantage to use one for the bulk of strength training.
Although he mentions that people should go beltless at least for the first few months. During that time, you should be building the fundamentals of strength training. Using a belt is a skill on its own and using one will just complicate things further.
To use the belt, just before performing the lift, inhale a huge breath in to your stomach. Push your stomach out in to the belt. Then keep that pressure during the rep.
Wrist wraps help keep the wrist straight. This helps keep the bar stable while squatting, and helps prevent it from sliding down your back. It helps keep your wrist straight during bench and overhead press.
They personally help me lift one or two extra reps than I could without them. This is because they help me maintain posture during the set. Though I don't use them often.
Used by people to help hold a bar during deadlift. I would say the best option is to not use the at all and use cross-grip or hook grip. See this answer.
They provide some support during squat by tightening up during the eccentric phase and provide some elastic "bounce" on the way up. They can be useful to help overload so you can lift extra weight than if you were not using them. Though they should not be used for majority of training. They also take practice applying.
These don't actually support your knees. Their main purpose is to keep your knees warm. They also provide compression and increase blood flow through the joint. In theory this prevents tendonitis (I personally haven't seen any studies that show this, but it's the general consensus from the pro-sleeve people).
I like using them while squatting because I think it feels good. Though you can get away with not using them. They tend to be expensive.
There are also some brands that provide some of that "bounce" that knee wraps provide, though not as severely. Powerlifters buy those for the simple reason is they do add a couple kg to the total and they fit regulation standards so you can use them in competition.