Learn Italian: Aspetto il treno. - I am waiting for the train.

In Italian, the verb aspettare already means "to wait for." You do not need to add an extra word like per to say you are waiting for something. You just connect the verb directly to the thing you are waiting for, like aspetto il treno.

How do I know this means "I am waiting" and not "I wait"?

In Italian, the regular present tense covers both meanings. Aspetto can mean "I wait" or "I am waiting" depending on the context. Here, since you are actively looking out for the train, "I am waiting" is the most natural English translation.

Where is the word for "I" in this sentence?

In Italian, you usually leave out subject pronouns like io (I) because the verb ending already tells us who is doing the action. The -o ending in aspetto makes it completely clear that "I" am the one doing the waiting.

How does the verb ending work here?

The verb aspettare is a regular -are verb. To make it match "I", you drop the -are ending from the dictionary form and add the "I" ending, which is -o. That is how aspettare becomes aspetto.