There are many methods to help with developing processes or testing processes. Therefore, we call them as part of software development methodologies and Software Development Life Cycle. The very basic one is PDCA which is Plan, Do, Check, Act.

The plan is to identify or collect requirements. The ways of collecting information as:
Surveys. To do surveys, we have more ways to get surveys:
-Interview
-On-Street
-Focus group
-Workshops
-Decision group
-Fill up a form
-Brainstorming
-Mind Map
-Prototype
-Analysis
The most popular one you might hear about for a plan is design thinking which included design persona, information collecting, prototype, and feedback.

The Do is to execute and coding the program. The Check is an analysis of the results if they match what we plan. Some companies include testing within the Do or within the Check. Then, the Act is based on the Check to enhance.

Later, based on the principle, people develop a lot of different process steps. The most popular ones are:
-Waterfall:
Requirements -> Design -> Implementation -> Verification -> Maintenance

-V-Model:
Requirement Design
System Design
Architecture Design
Module Design
Coding
Unit Test
Integration Test
System Test
Acceptance Test

-Iterative:
Initial plan
Plan
Requirement
Analysis Design
Implementation
Deployment
Testing
Evaluation

-Spiral:
Determine Objectives
Identify and Resolve Risks
Development and Test
Plan the next iteration

-Agile:
Plan
Design
Develop
Test
Release
Feedback

-LEAN:
Identify Value
Map the value stream
Create Flow
Establish Pull
Seek perfection

All the processes have their own purpose and spirits or the reasons why. For example, the waterfall is to know what is the next steps for developing; the V-model is to check if the testing is match design; the iterative is to build products in small parts; the Spiral is based on the features to build with the same orders; the agile is to build an MVP and communicated within all the steps; and, the LEAN is for customers to pull values and reduce all the wasting during the process. Therefore, it really depends on us to know the situations and use them wisely.