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Not sure how to play this. It's in the bass clef. My understanding is that the first curved line (green) is called a "slur," which means "move smoothly from note 1 to note 2." And the lower line is a "tie" which increases the count of the joined notes to the combined count of both.
But how do I move from the A in the first bar to the G in the second bar (slur) if I've already played the G in the first bar (now "tied" to the G in the second bar)?
how do I move from the A in the first bar to the G in the second bar
You don't. There is only 1 G note. Simply slur from A to G, and then hold the G for 3 beats.
Why are there 2 G note heads? Because notes can't go over a barline, so the composer had to notate it with 2 note heads connected by a tie. This is just a convention to enhance readability.
Why is the slur over both G's? This is also just a convention of notation, though I'm not entirely sure why. If you think of both note heads as being 1 note, then it makes some sense, no?
While they can look very similar, slurs are for articulation while ties are primarily for readability, so they operate on different planes, so to speak.
Play the A then smoothly start playing the G note, which, as you say, ties across the bar. Which means it doesn't get played again, purely held over for another two beats. The slur (or phrase mark) could have gone to the 1st G, but it's easier to understand the bigger picture if it expands to the end of the longer note, where the next slur (or phrase) starts.
The convention is that slurs start from the first of tied notes and end on the last of tied notes. Thus the slur covers both the endpoints. This convention makes it easier to quickly see the difference between ties (between time adjacent) notes and any pair of notes played legato.
