There are a lot of different ways you can achieve "3D" effects in web design. You can use CSS3 and/or Javascript for example to rotate text or other page elements in a 3D fashion. Here are some interesting examples with CSS:
20 stunning examples of CSS 3D transforms | CSS3 | Creative Bloq
There are also ways to create a "fake" 3D effect in Photoshop simply by duplicating a layer a bunch of times, and offsetting it by a pixel in a given direction each time, then merging the extra layers beneath the foremost one, into one layer of their own. You can seem some examples of that effect here:
Fake 3D in Photoshop | Photoshop | Web Designer
Photoshop also has real 3D rendering capabilities too, as I mentioned earlier.
The 3D tool in Adobe Illustrator is also pretty easy to work with, and since you are working in vector shapes, the images also have the advantage of being more lightweight and scalable at multiple screen resolutions.