Ask your broker to provide the legal forms. If you are changing beneficiaries in a joint account, you will need the notarized signature of the co-owner/spouse.
Stock holdings can be assigned to single or multiple beneficiaries. It is recommended that you seek council from an experienced estate attorney to set up a simple will or trust.
Contact the company where the stock was issued and ask for a beneficiary form. You will need to complete it and have the beneficiary sign it along with your signature.
When assigning a stock beneficiary, you will want to look at who you want exactly, and also contact your stockholder for information on assigning this person as the beneficiary.