The domain spells do not count against your number of prepared spells per day; they are extra, and always prepared (PHB, p. 58):
Once you gain a domain spell, you always have it prepared, and it doesn't count against the number of spells you can prepare each day.
You still cast them as normal, spending a spell slot. Divine Domain only gives you more spells to choose from, but no extra spell slots for casting them.
You choose only one domain when you get the Divine Domain class feature at 1st level, as it instructs (q.v.):
Choose one domain related to your deity
The people talking about choosing multiple domains are probably confused and misreading the advancement table and feature description. Divine Domain feature is listed as gained at multiple levels, but its description only lets you choose a domain when you get it at 1st level. The rest of the listings on the table are when its other benefits are gained (q.v.):
Your choice grants you domain spells and other features when you choose it at 1st level. It also grants you additional ways to use Channel Divinity when you gain that feature at 2nd level, and additional benefits at 6th, 8th, and 17th levels.