Usual length
The length of an independent study depends on the subject and assignment, but it's most often 10 to 30 pages. The exact number is usually set by the teacher — if it isn't, 15–20 pages is a reasonable average.
How it affects structure
At a smaller length (10 pages) usually 2 main questions are covered; at a larger one (25–30 pages), 3–4 questions, each given roughly equal space so the paper stays balanced.
Difference from an essay
The structure is nearly identical (outline, introduction, main body, conclusion, references), but an independent study is expected to have more of the student's own analysis and conclusions, while an essay mostly summarises sources.
How to choose a length
If no exact requirement is given, go by the subject's complexity: 10–15 pages tends to suit general subjects, 20–30 pages tends to suit specialised ones.