WHEN TO USE PHOTOSHOP
If you're dealing with photographs, you're most likely going to want to work in Photoshop — the name is the big hint. When you're retouching photos, digitally cleaning up a little dust from your camera lens, brightening photos that came out to dark in an otherwise sunny location, or cropping unnecessary background clutter out of the picture, you'll want to do it all in Photoshop.
WHEN TO USE ILLUSTRATOR
Illustrator is a "vector based" program, which means if you're planning on designing something in a vectorized style, such as a logo, or working mainly with type and text, Illustrator would be the best choice. With a few exceptions, think about "illustrating" something in Illustrator — one of the main tools used in Illustrator is the pen tool. It's a daunting tool that cause many users to shy away from the program, but once you start to understand how it works and play around with the pen tool, it's a fun thing to create things with, including shapes and abstract images.
WHEN TO USE INDESIGN
Generally understood to be a good platform to create multi-page documents in (e.g. books), InDesign is a good program where you can combine text and images. While you cannot heavily edit photos in InDesign like you can in Photoshop, if you want to combine photographs and text in flyers, posters, or small books, you can do this easily in InDesign. You'll be able to combine images and text without worrying about accidentally flattening layers (as in Photoshop) or directly affecting your photograph. If you think you have a basic understanding of Photoshop and Illustrator already, InDesign might be a good supplemental tool for you. This is a better alternative to programs such as Powerpoint (which should only be used for presentations, really) and Microsoft Publisher.
Let's not worry about InDesign for now and we'll focus on Photoshop and Illustrator first.
PHOTOSHOP VS. ILLUSTRATOR
While you can still type and edit text in Photoshop, text may be treated as a rasterized image in Photoshop in your final product, which might cause blurriness or pixelation on the edges of larger display sized text if you're not careful. But, If you think that you'll be doing more photo editing work than designing, then Photoshop will most likely be your answer.
Illustrator can produce sharper images and objects, but cannot edit photos. You can draw and create shapes and images in Illustrator using the pen or shape tools (you can do this in Photoshop as well, but it is much easier in Illustrator). While Illustrator can do limited 3D rendering, its generally best known for its ability to generate 2D (flat) images sharply, also known as vectorized images or objects. For example, pineapples, cucumbers, and oranges!