Well, this is ridiculous. I remember in version 3 there was a place to enable coupons as well as a place to set them up. In version 4, I've set up a bunch of coupons but can't for the life of me find how to enable them so there's actually a field for coupons in the shopping cart checkout process. Anyone? (I will ask support, too, just thought this might be faster, and it'll be a useful thing to have in the forum archives anyway.)
You can add Coupon brick to your signup form at aMember CP -> Configuration -> Forms Editor edit your signup form and add Coupon brick to it.
For the shopping cart: the coupon field is (I think) only displayed if the customer takes the long route: 'add to basket' before checkout. Then the coupon can be applied in 'view basket' or at checkout. If they use 'quick order', they have no chance to apply a coupon. So... if giving out coupons, either create a special order form with a coupon block, or issue careful instructions about how to order through the shopping cart.