IBA, IAA are both very good rooting homones. IAA (indole acetic acid) breaks down fast in open air and exposed to light but it is the most natural auxin you can get. It's also expensive and has a short shelf life. IBA (indole butyric acid) is more stable but has slightly less prominent effects. IAA and IBA both occur in plants, IAA being present in the highest concentration.
NAA (naphtalene acetic acid) is a compound regularly used when IBA/IAA are less effective.
Then there are a bunch of analogues with the same function but less described in literature. Most vegetative propagation papers, reviews and manuals include some rooting hormone. They start being effective at 0.02 mg/L or even lower. For woody plants, the concentration usually has to be a bit higher than that, with some pine (micro)propagation protocols going as high as 20g/L.
I get my IBA at home as a salt formulation with potassium. IBA-K. This salt is less effective than regular IBA because the potassium has some effects on the stability, but it's easier to dissolve in water without having to use HCl.
I have tubes of frozen NAA dissolved in KOH that I can use for whatever needs rooting.
Mix with water and apply as a foliar or contact-spray or soak the medium with it. Contact with open tissue causes the plant to easily absorb it. Some papers state that it takes less than 15 minutes for an actively growing plant to suck the auxins out of a solution.
Brands like Clonex have pretty high strength rooting gels, going up to 3g/L. Mix some of that with water and spray the foliage on a branch, you'll probably notice it'll behave differently. I use stuff like this as a rooting paint, instead of rooting powder that has dessicating properties; good for closing wounds, but bad for biological processes that are water bound.
The effect of rooting hormones are based on the plants genetic make up: some plants are very reactive, others need higher strength applications. Some plants respond to IBA, others to NAA. This response can change over time due to over exposure, so it might be good to use both and switch them every round of layering/taking cuttings from cuttings.
I base my concentrations on literature ("propagation of *plant name*" or "root formation *plant name*", "in vitro propagation of *plant name*", "induction of root *plant name*")
in general, the rule is as follows for all plants that share a common ancestor:
Low dose - increased rooting response, more roots overall compared to controls, more adventitious rooting (branching roots), small effect on shoot length and internode space.
Moderate dose - increased rooting response, more roots overall, visible effect on shoot length and internode space, can affect growth pattern in the sense that everything starts growing, higher biological activity due to cells being triggered to grow. Adventitious shoot/bud growth can be affected; both excitation (waking dormant buds) and inhibition (keeping them asleep) can occur. This is what happens in spring naturally.
High dose - sometimes an explosion of roots, sometimes total inhibition of rooting. Cell elongation is a fact, shoots might show giant internode spaces, foliage might be weaker and the plant might skip dormancy. Less budding, fewer adventitous shoots, and growth is focussed on the apex. High use of carbohydrates and resources due to increased growth activity. Lasts for about a month or two.
Extreme dose - total inhibition of rooting, stunted growth, shoots and other tissue expand so much that turgor pressure isn't enough to keep them upright. Callusses may occur at random spots. This might have lasting damage (4+ years).
Not every plant needs rooting hormones to root. I've tried to prove that the effects of auxins were minimal if the nutrient, vitamin and carbohydrate levels were met. I proved myself wrong. Rooting did occur in both trial groups, but the one with hormones performed faster, restored faster from injury, and showed an overall higher biological activity. The highest difference in rooting came down to roughly '500% more roots' in the treated group. Initially shoot growth was of lower quality, but after two weeks those effects diminished.
If there's something I haven't covered, feel free to ask.