"Execution" means putting your signature on it, having it witnessed and having your signature, and the witnesses signatures notarized. Your state laws will dictate how many witness signatures...
A codicil must follow the requirements of a will. Although the statute does not require a notary it always a good practice to have wills notarized.
32-1-104. Will other than holographic or...
A codicil is another document that amends a will in some fashion. The amendment could be a simple as changing executors or more extensive like adding or dropping beneficiaries. I must be signed in...