There are multiple different ways. These are only a few. They can also be mixed together.
(1).1 Bind the camera to a marker
You can do that by binding the camera to a marker on your timeline.
You can create markers on the timeline with the M key. Then select the camera you want to bind to that marker and hit Ctrl+B. As soon as your timeline reaches that marker the camera will switch. It is important that both the marker and the camera are selected.
(I forgot to turn the screencast keys on, see description above)
(1).2 Use multi-view (for stereoscopy)
You can enable multiple views in the Scene
tab of the Properties
panel. These are basically for stereoscopy-like effects, not for switching cameras, so I will only post a link to the manual: https://docs.blender.org/manual/en/dev/render/workflows/multiview/index.html
(2).1 Use the video sequence editor
The fancier (and maybe better) way is be to render the scene multiple times with the different cameras activated. Save the single frames in a lossless format. Then you can easily import them to the video sequence editor as strips and use the cross blend mode. You can then adjust the opacity value with keyframes (hover and I)
video sequence editor (old gif)
Edit:

In this animation I use the camera override
tool of the vse. You simply set up your scene and your cameras (with everything, including animations). Then in the video sequence editor add your scene strip multiple times (Shift+A) and set your camera override in the right panel.
Although I created a new scene (that was supposed to hold the scene strips). I forgot to switch back to that scene after switching to the vse. It is recommended to always use a separate scene for the sequencer! It may work in this example, but maybe not in bigger projects.
(2).2 Use the compositor
You can also add your frames to the compositor and mix them with very fancy effects. Then you can add this whole compositing scene to any video sequence editor. By the way: You can also add layers from other scenes directly to the compositor with the Render Layers
node. But then you need to copy your scene and if I got you correct this is not what you want.
It is possible that this is not what you want, so choose your tools wisely.
