9 times in 10 a vector image with realistic-looking shading made in Illustrator is made using the very powerful but rather tricky gradient mesh tool. It's not an easy tool to master and takes good judgement and patience to use well, but it's worth investing some time to learn.
The above link is a directory of 20 tutorials that should help give a head start.
As for the grainy texture, these kind of textures can be applied directly to the vector image using effects, which is a good approach as it maintains the vector image scalability - even if it's a raster effect, the effect will be automatically re-calculated at different sizes and resolutions. Here's an example tutorial.
Another alternate approach is to set up the base image in Illustrator then move to Photoshop to apply texture. This approach feels more free and natural, but isn't so good for long term scalability since you're creating a fixed resolution raster image. If you're working to a specified size, it's a good approach.
The designer James White uses this approach really well, and made this animated gif (with writeup) which illustrates it. The first step is the shapes in Illustrator with a a few brushes for basic texture, then the lighting and detail is painted on in Photoshop: