Unless it is absolutely necessary, it is best if you try to organically integrate the new information directly into the post (rewrite the entire post if needed). It is not necessary to keep all of the original post if it is not relevant, as the edit history will show what you original wrote (unless you are editing within the 5 minute grace period).
Posts that have long edit histories still in the post with Edit, Edit 2, Edit 3, etc are very difficult to read, and should be avoided.
One additional note for questions.
When editing questions, it is important you do not invalidate existing answers. It is a very fine line between clarifying your question and changing the question and you need to be careful not to cross it, especially if your question has answers.
The reason for this is that people have taken the time to answer your question and if you change the question, you could unintentionally open them up to downvotes from people who do not read the edit history and think they are not answering the question correctly.
For more info on this, please see Doesn't the asker have the right to modify his question? and the 2 top voted answers answers (full disclosure, one of the answers is mine but both have valuable info)