How to check if a user can access a given file?

To verify access visually, you can use

namei -m /path/to/really/long/directory/with/file/in

which will output all of the permissions in the path in a vertical list.

or

namei -l /path/to/really/long/directory/with/file/in

to list all owners and the permissions. Other answers explain how to verify this programmatically.

You can use bash to do this.

$ cat check-permissions.sh
#!/bin/bash
file=$1
# Handle non-absolute paths
if ! [[ "$file" == /* ]] ; then
    path=.
fi
dirname "$file" | tr '/' $'\n' | while read part ; do
    path="$path/$part"
    # Check for execute permissions
    if ! [[ -x "$path" ]] ; then
        echo "'$path' is blocking access."
    fi
done
if ! [[ -r "$file" ]] ; then
    echo "'$file' is not readable."
fi
$ ./check-permissions.sh /long/path/to/file.txt

To check this for a specific user, you can use sudo.

sudo -u joe ./check-permissions.sh /long/path/to/file.txt

If you have root access, impersonate the user, then run test -r (read), test -w (write), or test -x (execute) to check whether the user can read/write/execute the given file.

sudo -u otheruser test -w /file/to/test || {
   echo "otheruser cannot write the file"
   exit 1
}