This is how I understand it. The teams submit the trade to the NBA commissioners office, the trustees/league lawyers determine if a trade is legal, if so, it's official, and the players change teams. If a concern exists with a trade, the NBA board then requires approval from the board of trustees/owners and sometimes the NBAPA to over-ride a deal. If a player has a no-trade clause, the NBAPA designates with the player to confirm or deny to waive the clause.
Once two or more teams agree, the rest is done very quickly, like 10 minutes.
If a trade violates a rule, the NBA can then veto the trade. Like Chris Paul to the LA Lakaers(although that is a very different technicality). Trading a signed FA would be a NBAPA issue, not a board issue.