You can't contribute to someone else's IRA. It's an individual account, belonging only to the one owner.
You could give money to your grandchildren that they put in a Roth IRA. But the maximum contribution is $6000 or their income earned from working, whichever is less. So this won't be an option for young children. If you have an older grandchild with a job, you can support them by giving them money to put in a Roth IRA. However, it will be their money, and they could withdraw it at any time for any good or foolish reason.
If you give money to your grandchildren, it is not reported in any way on your tax return.
If you want to help your grandchildren invest but you still want to retain some financial control to keep them from spending it all on stupid stuff, you should talk to a financial advisor about the uniform gift to minors act and various kinds of trust accounts that are available for this purpose.
On the other hand, if you are talking about withdrawing money from your own Roth IRA and giving it to someone, that's certainly allowed. Roth IRAs are not taxable if you are over age 59-1/2, and the IRS does not care what you do with the money after you withdraw it. However again, if you want to make large gifts to your grandchildren, you might want to think about the UGMA and trust accounts.
