How to ask "How do you do?" in Latin.
Quomodo te habes, is it common?
What other common greetings for the "How are you?" exist?
I have seen:
- Quomodo es?
- Quid agis?
- Quomodo te habes?
I would not use quomodo es. It is a calque of the English phrase and does not strike me as sensible Latin. Of course, if someone finds attestations in reliable sources, I am ready to revert my opinion. Translated another way, quomodo es? is "in what way are you?", and that should give a hint at the unnatural nature of the phrase. Many idioms are unnatural but have become common, but the same turn of phrase is not necessarily sensible in all languages.
If you were to expand the English question "how are you?" to "how are you feeling?", you would get better translations. For example, ut vales? is a good way to ask for health, and it is the classically attested choice. Mind you that I would take that as an actual question, not a mere greeting. Quomodo te habes? and quomodo vales? are essentially synonymous to it but are more recent choices — I am only familiar with them as phrases used in contemporary Latin in Finland, and I claim no classical precedent. If you want to stick to what the Romans would have said, then ut vales? is the way to go.
Quid agis? is a good question, but it's more directly "what are you doing?". I wouldn't use it for "how do you do?" or "how are you?" but "what's up?".
Both ut vales? and quid agis? are classically attested phrases and therefore your best and safest choices. Both are found in the play Persa by Plautus.