One method is to go here and follow the instructions:
https://my.garmin.com/maps/chooseDeviceType.htm?But here are your options: the Nuvi will be eligible for an update because it had a map pre-installed. One time and lifetime updates are available, but you will probably do better to shop around. Check Amazon - you cannot actually buy the update from them, but you buy a code that is used to download the map on Garmin's site. Looks like the lifetime update is $54:
http://www.amazon.com/Garmin-nüMaps-Lifetime-America-Updates/dp/B001PKTFM8/ref=sr_1_4?ie=UTF8&qid=1352467757&sr=8-4&keywords=garmin+city+navigator+north+america+Numaps+updateCity Navigator is locked to a single device so you can't use the same map on the handheld however. Do you already have the DVD version of City Navigator for your handheld? If so, you should be able to purchase an update for it by going to your MyGarmin account if you have registered on their site. Since I don't have a DVD version myself, I don't know the exact procedure.
If you don't already have a DVD, you would need to purchase a new map. The cheapest way to get City Navigator for your handheld would be $60 for the "lower 49" version which doesn't include Canada or Alaska. This is only available by download and it cannot be updated in the future.
https://buy.garmin.com/shop/shop.do?cID=253&pID=28765If you have not yet registered either the Nuvi or the Handheld, do it now. Garmin will send you a 10% discount code you can use to purchase maps which will take the cost down to $54.
But if you want to update the maps on your handheld in the future, you should purchase the DVD version. Shop around for the best deal on the DVD, but it is $80 if purchased from Garmin (or $72 if you can get the 10% discount).