Make sure to add the proper tax class, select the country (or countries) and now very important: specify the "From total net" and "To total net".
If you leave both zero, the rule will be used flatrate for the country (which is probably what you want).
if you specify 0 to 1000 for example and the cart exceeds that net value, the rule won't fire and if there is no other matching one, it would assume that at this cart total net the shipping is free.
However, when set up correctly, you should see an option in the cart (not checkout) already to pre-pick a shipping option or tell the estimated shipping costs and say "Bases on the current cart value".
If there is nothing showing up in the cart, it means the system couldn't determine the country.
Either because the customer is not yet registered and/or logged in with all his address data OR there is no location plugin installed like Maxmind.
The very latest at the checkout, where the customer enters his address it should show the shipping price in the process. If there is also none, it basically means that no matching rule has been found (like I stated above).