Learn French: Il achète des vêtements, ensuite il va au restaurant. - He is buying clothes, then he is going to the restaurant.

The verb acheter (to buy) has a slight spelling change in the present tense to match how it is pronounced. For je, tu, il/elle/on, and ils/elles, that first e changes to è. For nous and vous, it stays a normal e (for example, nous achetons).

The translation just says "buying clothes", so why is des included in des vêtements?

In English, you can use a plural noun all by itself ("clothes"). In French, you almost always need an article in front of a noun. Des is the plural of un or une, acting like the word "some" (even though we usually leave "some" out in English).

Why is it au restaurant and not à le restaurant?

In French, the preposition à (meaning "to" or "at") and the masculine word le (meaning "the") are never allowed to sit next to each other. They always merge together to become the single word au.

The English translation says "is buying" and "is going". Where are the "-ing" words in French?

French doesn't have a separate "is doing" tense like English does! The standard present tense covers both meanings. So, il achète means both "he buys" and "he is buying", and il va means both "he goes" and "he is going".