how to use ping in a script

Use the -w switch (or -t on FreeBSD and OS X) on the ping command, then inspect the command's return value.

ping -w 1 $c
RETVAL=$?
if [ $RETVAL -eq 0 ]; then
    ssh $c 'check something'
fi

You may want to adjust the parameter you pass with -w if the hosts you're connecting to are far away and the latency is higher.

From man ping:

   -w deadline
          Specify  a  timeout, in seconds, before ping exits regardless of
          how many packets have been sent or received. In this  case  ping
          does  not  stop after count packet are sent, it waits either for
          deadline expire or until count probes are answered or  for  some
          error notification from network.

Use ping's return value:

for C in computers; do
  ping -q -c 1 $C && ssh $C 'check something'
done

ping will exit with value 0 if that single ping (-c 1) succceeds. On a ping timeout, or if $C cannot be resolved, it will exit with a non-zero value.

Not all network environments allow ping to go through (though many do) and not all hosts will answer a ping request. I would recommend not to use ping, but instead set the connect timeout for ssh:

for c in compuers; do
  ssh -o ConnectTimeout=2 $c 'check something'
done