Generally, you don't.
It's possible to write to another terminal, if you open a pair of xterms and run 'tty', on the first you can generate output (e.g. echo hi) and redirect it (>>) to the second terminals tty device file. Fiddling around like that is basically what the unix talk program does. So you could even have the script redirect the I/O of a command to another termianl; but in order to *actually* execute a program on the other terminal, you would have to setup a program on that terminal to handle the launching, and a way to communicate with it from your current terminal (e.g. through a named pipe or socket)
You probably do not want to do exactly what you asked how to do.
Thou shalt check the array bounds of all strings (indeed, all arrays), for surely where thou typest ``foo'' someone someday shall type ``supercalifragilisticexpialidocious''.