Quick answer
No entiendo
the everyday version
No comprendo
the alternative — see below for when
Which one to use
No entiendo is what people actually say. It covers everything from a word you missed to an explanation that made no sense.
No comprendo is correct but heavier and more formal, so it is better kept for written or serious contexts. If you simply did not hear the words, ask ¿Cómo? or ¿Puede repetir? instead.
All the versions
No entiendo.I don’t understand — the default.
No te entiendo.I don’t understand you — informal, one person.
No entiendo nada.I don’t understand anything — stronger.
¿Puede repetir, por favor?Can you repeat that, please? — formal.
¿Qué significa eso?What does that mean? — asking about a word.
Where you are matters
The wording barely changes by country; the main difference is <b>¿Cómo?</b> in Latin America versus <b>¿Perdona?</b> or <b>¿Mande?</b> in Spain and Mexico respectively.
Check yourself
Which phrase sounds most natural in everyday speech?