Photographs are 2-dimensional, but how sometimes you look at them, and they almost appear to be 3D. This is because in the 2D space of the image, the depth of the scene is also portrayed. Now generally, this is associated with expensive lenses, but you can give your images more depth by using some of the following tricks!
Shallow depth of field
This is where the expensive lenses come in, but you basically need to get as shallow a depth of field as your lens will allow. This means a low f/ number. By doing this you isolate your subject, but in doing so is only part of the process
Foreground and background
Just having a narrow depth of field does not give a lot of depth to the image; in fact it does the opposite, it can make images look a bit flat. What makes this work as a method is having foreground and background elements what are in the image but blurred out. So it is important to incorporate elements in foreground/background in order to give some perspective.
The scenes that work best are those with distinct layers that overlap. So try not only to get elements in the foreground and background, but at different intervals too.
Framing the subject
A great compositional method is framing. It basically means you frame your subject with other elements in the image. I have found that I use it a lot in wildlife, using a lot of foreground elements to frame the subject. It can really add some dimension to your images. So next time you are shooting, don't be afraid to use imposing elements in your shot to frame and emphasize your subject.
This is a common method to create depth in an image, as it basically works like an optical illusion. So, keep an eye out for converging lines in your composition! :)