I have a Roth IRA and Traditional IRA with Edward Jones. My account with Edward Jones says no 1099 tax forms will be generated (no taxable events). What should I report?

If you made contributions to either account, you do not need a tax form to report those.  Generally, the only tax forms generated for either a Traditional IRA or Roth IRA would be for some sort of distribution.  A Form 5498 is also generated later in the year, but it is not specifically reported as part of your tax return.

If you did make contributions to either or both accounts, see the following TurboTax help article to learn where to enter that information:

Where do I enter my traditional or Roth IRA contributions?