How do I file taxes when I got paid under the table. Example: cleaning houses, babysitting

It appears from what you say that you are an "independent contractor" doing various domestic tasks for a number of people. That is your business.

File a 1040 accompanied by a schedule C
http://www.irs.gov/pub/irs-pdf/f1040sc.pdf
And taking care to deduct every single expense from your gross wages.

Along with that file a 1040SE (self employment tax). Use the short form.
http://www.irs.gov/pub/irs-pdf/f1040sse.pdf

You can do without a W-2.