go to the www.usps.com web site and enter the country, weight, etc to get a shipping quote by each shipping service. you can also fill out the duty forms for customs. Be sure to designate the item as a gift or the recipient will be hit for customs duty.
you could also try fedex.com but for international I've found the USPS to be the cheapest. They have a flat rate international box you can pickup at the post office, but check you own packaging and choose the cheapest. The first $100 insurance is included in some shipping options, so before buying additional insurance be sure to read the details