If they gave you any "temporary" checks until yours arrive it would be the first 9 digits on the bottom of the check going from left to right. You can also contact your bank branch to get the number.
The routing number is the 9-digit number before your account number at the bottom on your personal check. The routing number, also called bank number is the number assigned to your bank, which is required for wiring and/or electronic transfer of funds.
Its the first set of numbers on the left hand side of the bottom of the check :)