if [[ -r $filename ]]; then
echo "$filename is a readable file"
fi
if [[ -w $filename ]]; then
echo "$filename is a writable file"
fi
if [[ -x $filename ]]; then
echo "$filename is an executable file"
fi
These tests take permissions and ownership into account to determine whether the script (or programs launched from the script) can access the file.
Beware of race conditions (TOCTOU): just because the test succeeds now doesn't mean that it's still valid on the next line. It's usually better to try to access a file, and handle the error, rather than test first and then have to handle the error anyway in case the file has changed in the meantime.