Bash Script using Grep to search for a pattern in a file

The single quotes around $pattern in the grep statement make the shell not resolve the shell variable so you should use double quotes.

Only one of those semicolons is necessary (the one before then), but I usually omit it and put then on a line by itself. You should put double quotes around the variable that you're echoing and around the variable holding your grep pattern. Variables that hold filenames should be quoted, also. You can have read display your prompt. You should use $() instead of backticks.

read -p "Enter file name..." fname
read -p "Enter the search pattern" pattern
if [ -f "$fname" ]
then
    result=$(grep -i "$pattern" "$fname")
    echo "$result"
fi