I am travelling in US (domestic), and have a one conformation number for 3 passengers, so I want all three of us sit together without paying anything.
Some tickets include free seat selection, others do not. That's a decision you need to make when you buy the ticket.
If your tickets do include free seat selection you can just picks seats online at the airline's website. Even with a single confirmation number, you can select seats for each passenger.
If your ticket does NOT include free seat selection you will have to pay for it.
If you don't have a reserved seat, you can pick one at check in from whatever is left. You can try to check in as early as possible and hope for the best but on most US domestic routes the chances of finding three empty seats next to each other during check in are slim.