Does a creature entering the battlefield trigger 'enters the battlefield' abilities if it is put directly onto the battlefield by a spell?

Whenever a permanent enters the battlefield, any abilities that trigger on that event will trigger. This is covered under CR 603.2, which states that triggered abilities trigger whenever the game state matches their trigger condition — including a creature entering the battlefield.

It does not matter how the creature arrived on the battlefield. Whether it was cast normally, put there by a spell like Sneak Attack or Aether Vial, or placed there by any other game effect, the creature still 'enters the battlefield' and all relevant triggered abilities will fire (CR 603.6).

Note that the creature itself may also have an 'enters the battlefield' (ETB) ability, and that ability will also trigger when it enters, regardless of how it got there (CR 603.3).

Example: You cast Elvish Piper and use its ability to put a Craterhoof Behemoth directly onto the battlefield from your hand. Even though you didn't cast Craterhoof, its ETB ability — giving your creatures +X/+X and trample — still triggers, because it entered the battlefield.

The only exceptions would be replacement effects (CR 614) that modify how a permanent enters — for instance, if a card specifies a creature 'enters the battlefield without its abilities' — but absent such effects, all ETB triggers fire normally.