I am trying to learn how to read sheet music for my guitar. I am starting with this beginner exercise, but I am confused on how I am supposed to know, for example, which F note to play when it comes up on the sheet music here (there are multiple F notes right?). How are you supposed to know which one it is referring to?
Because these exercises are to be played entirely in first position, each F indicated has only one option. The lowest F, for example (the second note of the first exercise), can only be played on the first fret of the 6th string.
Here's a chart that may be helpful:
© 1998, 2015 Jeffrey L Anvinson. Used by permission. Complete chart is available at: http://www.jlamusic.com/Learn/guitarnotes/naturalnotesfirstposition/naturalnotesfirstposition.html
It's worth mention that the website from which the OP image is taken includes lessons mapping written notes to finger positions. In particular, the "Guitar Method" page includes videos in the "Notes on the Guitar" section. In particular, the videos and pages "Notes in Open Position", "Notes in Fifth Position", and "Reading Low Ledger Lines" contain information that may be helpful.
Answering directly, there are 3 F notes in that music. Since the whole exercise is in first position, open, 1st, 2nd, 3rd 4th and for the very highest note, A, the 5th fret are used. There is only one place on guitar for the lowest F - the second note shown - and that is 6th string, 1st fret. The F in the bottom space of the stave is on 4th string, 3rd fret, and the F on the top line will be found by pressing the top string at the 1st fret.
True, there are often multiple places to play the same note, but since this is basic guitar tuition, one finger per fret, it's kept simple so each note is either an open string, or has a dedicated finger. Although you'll have to move your hand up two frets for the highest A note. Which makes me think the writer hasn't thought quite enough about what 1st position means.
You are in the first position and there is no duplicate of notes in the first position with the exception of the B on the 4th fret of the G string and the corresponding open string.
It is not enough to ask "what F do I play", you also want to understand which octave you are in. While there may be 3 F's in the first position they are each a different frequency, different octave, and each has a unique note in the music staff.
So, 3 ledger lines below the staff is first fret of the low E string.
The lowest space (Face, in F-A-C-E) is the 3rd fret of the D string.
The highest line in the staff (Fine, in E-G-B-D-F) is the first fret of the high E string.
Assuming standard tuning, there is NO other option for the lowest pitch F. The others will eventually have duplicates higher up the neck but never in the first position. As long as you are not moving up to the 5th position and beyond with this exercise every note is unique (again, with the exception of the aforementioned B).