Learn Hardcore Arabic (Levantine): حملت العفش الخفيف عالشاحنة. - I carried the light furniture onto the truck.

The verb حمل basically means to carry / lift / bear. In a sentence with a truck, English often prefers loaded, so something like loaded the light furniture onto the truck may sound more natural than a very literal carried the light furniture onto the truck.

So the Arabic verb itself is broad; the best English wording depends on context.

Who is doing the action in حملت?

By itself, حملت is ambiguous in normal Arabic spelling.

In Levantine, it can correspond to:

I carried / loaded
you (masculine singular) carried / loaded
she carried / loaded

Usually, the surrounding context tells you which one is meant. Arabic often drops subject pronouns because the verb already gives a lot of that information.

If you wanted to make it explicit, you could add:

أنا = I
إنت = you (masc. singular, in many dialects)
هي = she

Why is there no separate word for I or she in the sentence?

Because Arabic commonly allows the subject pronoun to be omitted.

This is very normal in Levantine. The verb form usually carries enough information, so speakers do not need to say or unless they want: