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

If the chosen creature has in its mana cost, that X is considered to be 0. The value of X in Altered Ego's last ability will be whatever value was chosen for X while casting Altered Ego.

X can be 0. Altered Ego won't enter with any additional +1/+1 counters, and it will just be a copy of the chosen creature.

You can choose not to copy anything. In that case, Altered Ego enters as a 0/0 creature and is probably put into the graveyard immediately. It won't have +1/+1 counters placed on it by its ability.

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

If the chosen creature is a token, Altered Ego copies the original characteristics of that token as stated by the effect that created that token. Altered Ego isn't a token.

Altered Ego copies exactly what was printed on the original creature (unless that creature is copying something else or is a token; see below). 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.

If you copy a double-faced creature, Altered Ego will be a copy of the face that's up when Altered Ego enters. Because Altered Ego is not a double-faced card, it won't be able to transform. If an effect instructs you to return it to the battlefield transformed when it leaves the battlefield, it won't return and will remain in its new zone.

If the chosen creature is copying something else (for example, if the chosen creature is another Altered Ego), then your Altered Ego enters as whatever the chosen creature copied.