With Shopify, you have the ability to show multiple currencies on your storefront for display purposes only. However, it is only possible at this time to checkout in one currency, the one selected in your Settings > General under the "Standards formats" section:
You can read more about showing multiple currencies on your store front in our wiki at: http://wiki.shopify.com/How_to_Show_Multiple_Currencies.
If you want your customer to be able to checkout in different currencies, you will need to open a second shop. Please contact our sales department using our contact form. Select "Sales Inquiry".