Learn Hardcore Spanish (Latin America): Sigo su rastro por el bosque tranquilo. - I follow his trail through the quiet forest.

Sigo is the first-person singular present tense of seguir, meaning “I follow” or “I continue.” Since the speaker is talking about themselves (“I follow his trail…”), you need the yo form, which is sigo.

What does su rastro mean, and who or what does su refer to?

Su is a possessive adjective that can mean “his,” “her,” “its,” “your (formal),” or “their.” Rastro means “trail,” “track,” or “trace.” So su rastro means “his/her/its/your/their trail.” You pick the referent of su from context (for example, an animal, person, or group).

What’s the difference between rastro and huella?

Rastro is a general “trail” or set of “traces” left behind (footprints, scent, broken branches).
Huella usually means a “footprint” or “paw print,” a single mark.
Here, rastro is more natural if you’re following a sequence of signs rather than one print.

Why is por used in por el bosque tranquilo? Could I use a través de instead?

Por indicates movement through a location or along a path: “through the forest.”
A través de also means “across” or “through,” but is more formal or literal (“across from side to side”).
You could say Sigo su rastro a través del bosque tranquilo, but most speakers prefer the simpler por.

Why does tranquilo come after bosque? Could I say tranquilo bosque?

In Spanish, descriptive adjectives normally follow the noun: bosque tranquilo (“quiet forest”). Putting tranquilo before the noun (as in tranquilo bosque) is grammatically possible but gives a more poetic or emphatic tone, not the typical neutral description.

Can I express the same idea using the progressive, like Estoy siguiendo su rastro por el bosque tranquilo?

Yes. Estoy siguiendo su rastro… uses the present progressive (“I am following its trail…”), emphasizing the action right now. Sigo su rastro… (simple present) is more general or habitual (“I follow its trail…”), but both are correct and understood.