'shows the process' is correct and can be used in written English.
For example, you could write, "This diagram shows the process of photosynthesis."
There's a video that shows the process in detail.
A lot of historical evidence shows the process is a painful one.
The following pictures shows the process that we use mouse to make the selection.
The video shows the process by which Kendall came to create her own narration for the video we're watching.
This is not very alarmist language, and the company claims that it shows the process is working as designed.
The poem is an autobiography; it shows the process by which he comes to know the world around him.
This chapter shows the process of mapping from a Java PSM to Java code.
Independently verified data shows the process Drax has developed produces an 86 per cent carbon saving against using coal.
Here's a great video that shows the process in action.
Figure 4 shows the process of reconstruction.
Figure 5 schematically shows the process.
