IANAL, but I've dealt with this situation and my key takeaways are as follows:
1. Pay a lawyer to read the document for you and provide advice.
2. There are major differences in state law, and jurisdiction is important. For example, if you worked for Google in NY[0], and your contract was a NY-based contract, and there was a harsh noncompete in it[1], and you subsequently took a job in California that violated the terms of the non-compete, it doesn't matter that your new job is in California and Google's HQ is in California and Alphabet is domiciled in Delaware. You signed, and are potentially in violation of, a contract whose potential violation would be adjudicated in New York.
3. Upon receiving advice from your lawyer, and bearing in mind the importance of state jurisdiction, ask your former employer to make changes to the agreement as you see fit, especially if there is an aggressively worded non-compete.
4. Don't believe them when they say "this is just a formality". Read the fine print and understand what it means.
[0]: Has already been mentioned a couple times in this thread, but California is a much more employee-friendly state than NY. Non-competes are essentially unenforceable, as are non-poach agreements. It's my understanding that disparagement clauses are also a lot harder to enforce in CA, but IANAL.
[1]: To be clear, I am not sure whether this would be the case at Google specifically, just using a well-known California-based company as an example.