Your parent can't give you title to his IRA as if it were the family car. There's no way to transfer ownership of the account to you until after he passes on. He may, however, be able to tap the IRA assets for your benefit or find other ways to help you while he's still alive.
The one way your parent can give you full ownership of his IRA is to name you as the beneficiary on the account. When he dies, you inherit the IRA assets without going through probate. Unfortunately, you can only withdraw money -- you can't put any more in. You have to make annual minimum withdrawals, usually basing them on IRS life-expectancy tables. If you need money, you can withdraw more than the minimum, but the more you take out, the more tax you pay.
Starting an Account
If you work, even if it's only part-time during college, your parent can help you fund an IRA. You may not be able to spare any money to contribute to a retirement account, but if your parents give you a cash gift, you can deposit that extra income. Federal rules say you can deposit up to $5,000 a year or your total earned income, whichever is less. That's why you have to be working to deposit a gift: If you don't earn any money, your contribution limit is zero.
Your parent can't give you his IRA, but he can give you some or all of what he withdraws from it. He can begin taking money out when he reaches 59 1/2. If it's a Roth IRA, there's no tax on withdrawals, and he can give you up to $13,000 in withdrawn income a year without paying gift tax. If it's a traditional IRA, he will pay tax on whatever he takes out. If there's a charity you're passionate about and your parent is older than 70 1/2, he can withdraw up to $100,000 a year for donations without paying tax.
If you'd like to set up an IRA for your own child, the younger she is, the better. The more time the money sits in her account, the more interest it's going to accumulate by the time she start withdrawals. Forbes recommends starting her with a Roth IRA as soon as she's earning enough money. Her income should be low enough that she won't pay much in tax on the contributions, and her later withdrawals will be completely tax-free.