Learn Russian: Сегодня магазин даёт хорошую скидку. - Today the shop is offering a good discount.

It is in the accusative case because it describes the direct object, скидку (discount). For feminine adjectives, the dictionary ending -ая changes to -ую in the accusative.

Why is the noun spelled скидку instead of the dictionary form скидка?

Скидка is the direct object of the verb даёт (the shop is giving a discount), so it must be in the accusative case. Feminine nouns ending in -а change their ending to -у.

The English translation says 'is offering', but doesn't даёт mean 'gives'?

Yes, даёт literally means 'gives' or 'is giving'. In Russian, the standard way to say 'to offer a discount' is давать скидку (to give a discount).

What is the infinitive of даёт, and why did it lose the 'ва' in the middle?

The infinitive is давать (to give). It is a common irregular verb where the -ва- drops out completely when you conjugate it in the present tense, which is why we get даю, даёшь, and даёт.