As mainframer said, you can use grep, but i would use exit status for testing, try this:
#!/bin/bash
# Test if anotherstring is contained in teststring
teststring="put you string here"
anotherstring="string"
echo ${teststring} | grep --quiet "${anotherstring}"
# Exit status 0 means anotherstring was found
# Exit status 1 means anotherstring was not found
if [ $? = 1 ]
then
echo "$anotherstring was not found"
fi