If your spouse doesn't have much of a credit history, adding him to your credit card can help. When you name your spouse as an authorized user on your credit card, you are responsible for any bills he runs up. Your spouse can then start building his own credit history.
Adding your spouse as an authorized user is simple. Call the credit card company, ask it to issue a card to your spouse on your account, and you're done. When the card arrives, your spouse can use it to make purchases on your account. Paying your bill on time then improves her credit history as well as yours. Some credit-scoring systems won't include her authorized card when scoring credit, though, as she's not liable for the debts.
Turning your credit card into a joint account with your spouse is a bigger deal than adding an authorized user. If you request the credit card company change your account to add another name, the company will want to review your spouse's credit score and history before agreeing to add his name. As joint account holders, you're both liable for the monthly bills, no matter which of you actually run them up.
The risk of opening your credit card to your spouse is that she might make purchases for which you must pay. When she has her own card, you're not liable for her debts if she dies. If she's on your card, or if the two of you have a joint account, the credit card company will look to you for satisfaction. Additionally, the company may lower your credit limit and raise your interest rate.
If putting your spouse on your card is just to improve his credit history, you can add his name without handing him a card. That way he gets the benefit of being on a regularly paid account, but there's no risk to you. If the intent is practical -- a common account for paying grocery bills, say -- opening a new joint account with a low credit limit protects you both against the other going on a spending spree.