Time: about 30 minutes.
Take Route 1 from Tel Aviv towards Jerusalem. Exit at Ben Shemen Jct. for Route 443; the sign will say "Modiin". The exit comes just after the exits for Route 40. Continue on Route 443 for about 5-10 minutes until you reach Shilat Jct. Turn right for the main entrance to Modiin. (For your information, this route does not cross the Green Line.)
Time: about 30 minutes.
Take Route 1 from Jerusalem and exit at Latrun Jct. At the end of the exit ramp, turn right towards Modiin. This will take you through Park Canada (Ayalon Park). Follow the highway (Route 3) past Park Canada. A couple minutes later you'll come to a left turn with a sign for Modiin. Turn left there. Follow this road for about five minutes until you enter Modiin.
(the Ramot / Givat Zeev / Bet Horon road; passes through the "territories" for about 15 minutes)
Time: about 30 minutes.
Take Route 443 from Jerusalem, past Givat Zeev and Bet Horon. About five minutes after Bet Horon you'll pass the checkpoint leaving the territories. Continue to the second traffic light and make a left at Shilat Jct. at the main entrance to Modiin.
Time: about 1 hour 10 minutes.
Take Route 40 north from Beersheva. At Re'em Jct. turn right onto Route 3, which should be signposted for Modiin. Follow Route 3 past Latrun Jct. Continue through Park Canada, A couple minutes later you'll come to a left turn with a sign for Modiin. Turn left there. Follow this road for about five minutes until you enter Modiin.
There is no train station in Modiin yet, but Margalit buses run between Modiin and the following train stations: