Lai,
The basic formula is:
Cén chaoi a bhfuil tú?
Tá mé go maith, slán a bheas tú. Cén chaoi a bhfuil tusa?
Tá mise go han-mhaith, slán go raibh tusa.
"How are you?
I'm well, thank you. How are you?
I'm very well, thank you.
(Here, "thank you" is literally "may you be healthy/safe")
Into that you can substitute macdara's elaborations. You may also encounter:
Tá mé réasúnta maith. "I'm reasonably well"
Go measartha. "Middling"
Níl mé ró-mhaith ar chor ar bith, dháiríre. "I'm not too well at all, really."
In that case you might like to ask:
Céard atá ort? "What's the matter? What's troubling you?"