I had a monster reply typed but stupid "alpha quality" Firefox decided to poop out on me. Anyway, short version the way I understood the question. There may be multiple interpretations thanks to the wording or lack of.
Run the program in the same terminal and have it still useable:
Sameas above but dump all that annoying output to a file rather than have it in your terminal:
/usr/bin/aircrack-ng &>~/aircrack-output.txt &
and truly in a new window:
xterm -e /usr/bin/aircrack-ng