As you read The BFG by Roald Dahl, you will discover two descriptions of the dream-catching process, one narrated by the BFG talking to Sophie, which is the less detailed of the two, and one recounted through the viewpoint of Sophie herself as she accompanies the BFG on a dream-catching expedition.
The first step is that the BFG travels to Dream Country. He has very sensitive ears that enable him to listen for dreams, and locate them by sound, as they are invisible. He catches the dreams in a butterfly net and then transfers them into jars, just as a butterfly catcher would catch butterflies. Once the dreams are in the jars, they become marginally visible. The BFG is capable of mixing dreams together to create new dreams. He blows dreams toward people (or other giants) to make them experience the dreams.