How does one write a script to do some work on all DB's?

All databases on your machine should be listed in the ORATAB file. One can use this information to do processing on all databases on your machine. Look at this example:

#!/bin/ksh
ALL_DATABASES=`cat /etc/oratab|grep -v "^#"|grep -v "N$"|cut -f1 -d: -s`
for DB in $ALL_DATABASES
do
   unset  TWO_TASK
   export ORACLE_SID=$DB
   export ORACLE_HOME=`grep "^${DB}:" /etc/oratab|cut -d: -f2 -s`
   export PATH=$ORACLE_HOME/bin:$PATH
   echo "---> Database $ORACLE_SID, using home $ORACLE_HOME"
   sqlplus -s system/${DB}password @<<-EOF
      select * from global_name;
      exit;
      EOF
done

NOTE: The terminating 'EOF' should normally be in column 1. The '-' before the first EOF above causes the shell to strip all leading TAB characters (not spaces, only TABs) from that point until (and including the EOF). This lets you indent the code in between using TABs.