Why is shipping showing as zero at checkout?

Check these on Settings → Store Settings → Shipping Setup:

• Offer free shipping above a minimum order amount is ticked with Minimum Order Amount for Free Shipping at 0. Every order then ships free.
• Shipping Type is Per Product, but the products have no Shipping cost. Also, in this mode shipping is taken out of the price, not added on top.
• Overall Product is selected with Shipping Cost empty or 0.

Other things that make shipping free:

• a Free shipping coupon
• a customer group with Free shipping for this group
• a zone method set to Free shipping, or with Free above cart total reached

Fix the cause and click Save Changes.