Often, the initial drop cap in a paragraph is a different font or colour from the rest of the paragraph. One way to achieve this is to create a character style and then apply the character style manually to the drop cap character(s).
InDesign also allows you to nest the character style in a paragraph style which is a much quicker method.
Setting a character style for drop caps
You can also apply other nested character styles to any characters following the drop cap, using the New Nested Style option.