Write a Python function that attempts to open a file and read its contents. The function should handle exceptions that arise if the file does not exist or if there is an error reading the file.
Explanation of Solution: The function read_file attempts to open the specified file and read its contents. If the file does not exist, a FileNotFoundError will be raised, and the function will print a message stating that the file does not exist. If there is an error reading the file, an IOError will be raised, and the function will print a message stating that there was an error reading the file.