I don't know of any free bookkeeping courses that would be of any value.
I would recommend taking a few courses at your local junior college if you are serious about opening a bookkeeping service. You will have a very hard time finding clients if you don't know what you are doing.
I would suggest taking at least one basic accouting course, a course in Excel and a course in Payroll Accounting if you plan on doing payroll.
Also, I highly suggest a course in QuickBooks or, better yet, becoming a QuickBooks ProAdvisor. You can check into that at www.quickbooks.com. There are a lot of people on QuickBooks and knowing how to set-up and use this program is a big plus.
You will need to check with your state regarding sales taxes and payroll taxes to see what is due and when. Sales taxes need to be paid once a month and payroll taxes usually every month or quarter. Check out the IRS website as well for payroll taxes. You will learn about this in Payroll accounting.
TIP: If you cannot afford the courses - find out what book they are using and study it yourself. You may be able to purchase the book cheaper on Ebay.
I would also like to recommend the American Institute of Professional Bookkeepers at www.aipb.com. They have great books that you can study and you can also become a certified bookkeeper.
Good luck!