From North America you will have to fly to Scotland, Iceland or Denmark and change for the Faroes there. There are currently no round the world fares from Australia or New Zealand that include the Faroe Islands, so if you're coming from the Antipodes you'll similarly have to fly to Europe first. You can take ferries between May and early September from Norway, Iceland and Denmark, and although it takes more time than flying and isn't particularly economical, it is still a pleasant way to get there.
Roads are surfaced and the difficult parts have been bypassed by tunnelling through mountains.
The only inter-island travel by air in the Faroes is by helicopter, and it's a surprisingly cheap way to island hop. As flights are normally booked out, it's wise to reserve seats weeks in advance. When combined with the ferry services, it links virtually every corner of the islands. The fares are steep and add up quickly if you're doing a lot of travel, but you can get a transport pass that gives reasonable discounts. Driving yourself around the islands is easy, but unless you're bringing your own car, hiring a vehicle is expensive.