1. Place your cursor in only the first paragraph. You don't even have to highlight the entire paragraph. Just make sure the first paragraph is the only paragraph highlighted.
2. Apply the drop cap feature/paragraph style. In this case, it will only be applied to the first paragraph.
To apply the style on the fly, create a new paragraph style called Drop Cap with your drop cap style, and another called No Drop Cap with all the type attributes of the first style, except with no drop cap attributes. Then go back to the Drop Cap paragraph style and choose the No Drop Cap style from the Next Style: options box. As others have said here, that will apply the drop cap to the first paragraph and no drop caps to subsequent paragraphs when you highlight it all and apply the style.
Hope this helps,
Randy