How do I access a new annuity account?

The first thing you should do is present this question to your financial advisor.

If you don't have a formal, ongoing relationship with a financial advisor, then talk to the person who sold the annuity to you.

You can also present the question to the insurance company that provides the annuity.

The insurance company will have the most detail because an annuity is a contract between you and the insurance company.  The contract is provided by the insurance company and it lays-out (in great detail) how the thing works.

The above said, for day-to-day stuff you should have some sort of financial advisor relationship.  Again, the person who sold the annuity to you is the natural starting point.

Web access, brochures, beneficiary forms, contract details, account access, mutual fund info (with variable annuities), etc will likely be communicated through some combination of a financial advisor and the insurance company that provides the actual product.