What do I need to set up to ship to other countries?

Work through these in order:

1. Settings → Store Settings → Selling Location: add each country you'll ship to. Checkout only lists countries you've added here (when none are added, it lists every country).
2. Shipping price: manual shipping charges the same amount everywhere. For a different price abroad, use the Shipping Zone plugin: create a zone whose Regions are the foreign countries and give it its own methods.
3. Settings → Store Settings → Manage Tax: add rates for the new countries if you need to charge tax there. Rates can only be added for your selling countries.
4. Currency: with the Multiple Currencies plugin, shoppers can see prices in their own currency.
5. Labels: with the Shipping Carriers plugin, a label-capable carrier that ships internationally, such as UPS or Envia, can create shipments from the order page.

Place a test order with a foreign address before announcing it.