How do I make things explode, or burn in 3D??

Answer 1

The short answer is that you cannot use just one piece of software.

Remember when it comes to making Special Effects (SFX) is to always use several different software types to achieve the effect. Trying to do everything in one software leads to a lot of wasted time and less than stellar results. You mention 3D which means you want debris to be flying. Blender has an excellent particle tool called "Fracture". This breaks up the model without a lot of effort on your part and when combined with other dynamic forces, resulting smaller objects can be hurled realistically.

You can also create smoke and fire but it needs to generated separately and then "composited into the scene". AfterEffects is a great compositing software that gives full control to how thick the dust and smoke will be.

The key to a good scene is to render everything separate.