Any enters-the-battlefield abilities of the copied creature will trigger when Sakashima enters the battlefield. Any "as [this creature] enters the battlefield" or "[this creature] enters the battlefield with" abilities of the chosen creature will also work.

If Sakashima is your commander, it remains your commander even if it's copying another creature. If Sakashima is not your commander, it remains not your commander even if it's copying your commander.

If Sakashima somehow enters the battlefield at the same time as another creature, it can't become a copy of that creature. You may choose only a creature that's already on the battlefield.

If another creature becomes a copy of Sakashima, that creature also has Sakashima's other abilities.

If the chosen creature has {X} in its mana cost, X is considered to be 0.

If the chosen creature is a token, Sakashima copies the original characteristics of that token as stated by the effect that put that token onto the battlefield. Sakashima doesn't become a token in this case.

If the chosen creature is copying something else, then Sakashima enters the battlefield as whatever the chosen creature copied.

If you control more than one legendary permanent with the same name and the "legend rule" begins applying again (perhaps because Sakashima of a Thousand Faces leaves the battlefield), you'll immediately have to comply with the rule and put all but one of those permanents into the graveyard.

Sakashima of a Thousand Faces copies exactly what was printed on the original creature (unless that creature is copying something else or is a token; see below), except that it also has Sakashima's other abilities. It doesn't copy whether that creature is tapped or untapped, whether it has any counters on it or any Auras and Equipment attached to it, or any non-copy effects that have changed its power, toughness, types, color, or so on. Most notably, if it copies a creature that's not normally a creature, it won't be a creature.

The "legend rule" is the rule that states that if a player controls two or more legendary permanents with the same name, that player chooses one of them, and the rest are put into their owners' graveyards. (704.5j at the time of this document's creation for those of you scoring at home.)

While the "legend rule" doesn't apply to permanents you control, you can control any number of legendary permanents with the same name and none of them will be put into the graveyard.