splitting field into 2

I am working with Access tables given to me by a client and incorporating
their data into a larger database. The old tables have the first name and
last name in one field, which most of us know it's a no-no in database world.
The last name is first, followed by a comma (no space), then the first name.
Here's an example, "Smith,John".

How can I separate the last name into its own field and likewise for the
first name? The lengths of the names vary, so it's not possible to specify
the number of characters in using Left, Mid, or Right coding. Is there a way
to use the comma as a separator?

Thank you!