I have heard that I should establish credit in my own name before telling the credit card company that my husband has died. How do I do this?

If you maintained a joint account with your husband you have already
established your own credit history, if you were an authorized user with no legal responsibility to pay the account balance this will not help establish your own credit history. Hopefully, you have established a credit history separate from your husbands and will not have trouble obtaining your own card. If you don't have your own credit history you may want to establish a bank account in your own name and apply for a new card in your name. If you have difficulty obtaining a credit card, you can always obtain a secured card or have someone co-sign for a joint account.

If you would like to check your credit report below are the main credit bureaus:
Equifax (800)-685-1111, Experian (888) 397-3742, Transunion (800) 916-8800.