Let's explain using G13 as example.
We start with the basic G major triad: G/B/D and the than we stack thirds on top of it. So G7 would be G/B/D/F, G9=G/B/D/F/A, G11=G/B/D/F/A/C, and finally G13=G/B/D/F/A/C/E
At this point the chord includes all notes in the C major scale, i.e. all the white keys on the keyboard. You can simply take a 2x4 and press down as many white keys as you can. If someone asks "what the heck are you playing?" you can answer "Why, dear sir or madam, that is a G13 chord" and you'd be theoretically correct.
In practice you will still get kicked out of the band, since it sounds terrible. It also poses a problem for guitar players: there are seven notes in the chord and you have only six string.
Obviously you don't play all the notes. Most chords have a key "tension" interval that creates the character of the chord. Make sure you capture this. You also want to include the third just to make sure you can distinguish between a major and a minor key.
For the G13 the tension interval is 13 vs 7, i.e. E vs F. You also want the E on top, hence you write it as a 13 and NOT as a 6. For grins you can try playing the F on top as well: You ears will NOT be pleased! The other chord notes are optional and can either add flavor or clutter things up depending on what else is happening.
So in this example your minimum set a good choice of notes for a G13 would be G B F E and that's probably what the person who scribbled G13 on the chart intended. If you have a competent bass instrument in the band, you can also drop the root and simplify further.