You do not need to memorize the whole neck at once. Choose a short stretch of four or five frets and find the available notes on each string. These local patterns are often called positions or boxes.
A fingering position is not itself a mode. You can play C Ionian and A Aeolian in the same area of the neck; the tonal center and musical context determine what you hear.
Use comfortable fingering, keep your hand relaxed, and connect neighboring positions gradually. The best fingering depends on the phrase, the stretch, and your hand.
Pick up your guitar
In A Aeolian, explore frets 5–8. Play just three notes, then repeat them with a different rhythm.