Read the symbol in two parts
In a symbol such as C over E, written C/E, the part before the slash names the chord and the part after it names the intended bass note. It does not mean play C and then E major. The E belongs beneath a C major harmony. Listen to the recording for the bass direction that the symbol describes. A sequence of inversions often creates a smooth rising or falling line even when the upper chord tones change very little between measures.
Check what your guitar can provide
Find a comfortable C voicing with E as the lowest sounding note. Open low E is a valid bass for C/E when that register suits the arrangement; avoid accidentally adding a lower note that changes the intended bass. Some slash chords fit open shapes easily; others require selective string picking or a smaller voicing. If a bass player supplies the written bass note, your guitar may only need the upper chord. Agree on this division rather than making every instrument duplicate the same low movement throughout the passage.
Practice the line before the full texture
Play the bass notes alone in rhythm and sing their contour. Then add the smallest chord voicings that support them. Compare the result with your AudioChords chart and verify any unexpected slash label by ear, since a passing bass note may not require a new sustained chord. Keep the timing of the line clear before adding a full strum. In a solo arrangement, preserving the bass direction can be more important than including every doubled chord tone. Make that choice consciously and listen to the melody to confirm that the reduction still supports the phrase.