Although it can vary (slightly) by state, generally speaking the state filing instructions invariably say to attach pages 1 and 2 of your Form 1040 (or 1040A), or just the first page of your Form 1040EZ.
Additionally, you should usually include any Schedule A (Itemized Deductions) if you have such a page (and since more than 2 in 3 taxpayers don't itemize deductions, you may very well not have one). Also, you will want to attach any W-2 or Form 1099 statements, if they show any state taxes withheld.
Finally, you should include with your state return any other state-specific pages that print with the TurboTax program (other than the filing instructions cover page itself).
Thank you for asking about this.