If you have to transfer a Roth or traditional IRA to your spouse, that's bad news. You can't just give your spouse your IRA as a gift: the only time you can transfer ownership is when you're splitting up your assets as part of a divorce. If you follow the federal rules, there's no tax on the transfer.
To transfer a Roth in divorce you need something in writing. A post- or prenuptial agreement or a divorce order requiring you give up the account will do the trick. You can also divide it so that your spouse gets part, but not all the assets. This is different from just writing her a check for the value of the Roth. With a divorce transfer, she can manage the account just as if she'd owned it from the start.
You can't transfer your Roth until the divorce is final. If you're giving up the entire account, the simplest way to do it is direct your account trustee to change the owner's name from yours to your spouse's. If you're dividing the account, you can have the trustee transfer some of the assets to your spouse's Roth, either a new one or an established account. You can also change the name to your spouse's and transfer your remaining share to a new Roth of your own.
If you don't follow the required procedure -- for example, you write your spouse a check or you transfer ownership before the divorce is over -- the IRS can treat the transfer as if you made a regular withdrawal. That's not as bad with a Roth as a traditional account because you can make withdrawals tax-free, up to the limit of your original contributions. If you take out your earnings as well, and you're younger than 59 1/2, however, you pay tax.
In most divorces, the court's goal is to divide property fairly between spouses. This gets tricky if, say, your spouse gets your Roth in return for you keeping the house. You can turn a profit on the sale of the house immediately, but your spouse may not start withdrawing from the Roth for years. The relative value of the two investments depends on how the Roth grows between now and then. That's hard to predict.