As mentioned in the other answers, you should include the fees in your project's price. It should not be charged as extra.
But if the client requests a special payment method that is not part of your standard payment methods then yes you can ask for an extra. For example, you have a merchant account but the client still wants to use Paypal or Western Union, you can specify there will be additional charges. That is often seen on many websites of big corporations, especially with Paypal payments. One benefit of doing this is the client might decide to use your favorite payment method instead of the one with the extra charges.
But if you offer only one payment method, then no, you don't ask for transfer fees or any other fee related to this; that's part of your responsibilities to include this in your project's cost and price.
As to how to ask for the extra charges, I think this should be done during a communication before sending the invoice. You don't ask clients to calculate their own fees; you do it. Best way to do this is by asking by email "what method of payment they prefer to use" and then offer them your choices and explain the fees without extra justifications. Then prepare the invoice accordingly. This can be asked while they ask you for a quote too, before you start the project; it's fair.
If you use an online way of collecting the payments and it can be done by adding buttons (for example), then simply do as any other corporation do and add a note below the Paypal button saying something like "10% extra transfer fee applies." It doesn't matter how you say it, people are used to this and it doesn't require any justifications when there's more than one option to make a payment.