How can I create these types of gradient images in Illustrator?
The procedure to create complex gradient is eventually pretty easy.
Sep 1) Create a rectangle the size of your canvas, with no stroke or fill
Step 2) Now you need to create what is called "Gradient Mesh"! You'll find its icon in the toolbar.
Step 3) with the tool active, simply click where you want to add a pivot (sort of control point) inside the rectangle. You can then associate a colour to every single pivot (you should select the pivot and click on the color panel to choose the color, or if you want to duplicated some picture - choose color picker and click on the picture to be copied): Illustrator will create a nice smooth transition in between every shift of colour.
Step 4) if you need it, you can refine the position of the pivots and their colours.
Step 5) Job's done!
EDITION (Ilan, picture added) Creating/duplicating of the picture in question took 1 minute -