The card with upgrade moves to the battlefield, but it doesn’t enter the battlefield. Instead it overlays an artifact you control. That artifact becomes represented by the new card – if it was tapped, it’s still tapped; if it had counters on it, it still has those counters; if it was attacking, it’s still attacking; and so on.

Enters-the-battlefield triggers won’t trigger when an artifact with upgrade overlays another artifact.

If you can’t choose an artifact you control while applying a permanent’s upgrade replacement effect, it doesn’t move to or enter the battlefield at all and instead moves to exile.

An artifact can be upgraded more than once.

If the upgraded object moves to the top or bottom of its owner’s library, that player chooses the relative order for its component cards without revealing that order.

If a player’s commander is upgraded, the resulting creature is still their commander. If it leaves the battlefield, the commander can be put into the command zone instead, and the other cards move to the expected zone.