Go the Alerts like you were going to set  one for yourself and just type
in another user's name.

We had the same question from our end users  - turns out that
the "Design" permission level doesn't have enough permissions by
default.

To modify -> In the list of permission levels, click the name of
the "Design" permission level. In the list of permissions, select the
check box to add "Manage Alerts."

Once that has been modified users that have "Full Control"
and "Design" permissions can add alerts for others.