For the federal amended return, include only Form 1040-X and any forms or schedules that have changed or are added. Do not include a copy of the original return. For more details see the IRS Instructions for Form 1040-X, especially "Assembling Your Return" on page 11.
For New Jersey see "Enclosures with Form NJ-1040X" on page 1 of the Instructions for Form NJ-1040X. Do not use staples, paper clips, or anything else to fasten the pages. Just put all of the pages loose in the envelope.
