First of all, you need to define the problem. This involves gathering the requirements of the assignment.

After that, you analyse them. Here you should think about constraints, objects, processes and potential obstacles related to the problem. Based on a deeper understanding of the problem, you can extract the important information from the requirements and discard the non-important information, and explore its properties, which will be useful for building a solution.

The next step is to identify several solutions. You try to generate and explore different ideas and technical approaches on how to build a well-working solution. Then you analyse these ideas, their correctness, their strengths and weaknesses, their practical applicability and the costs of their implementation.   

After you have gathered some ideas you need to choose one of them. This is a decision-making process and depends mainly on the requirements, your capabilities and available resources.

After that, you need to plan and describe your actions for executing the chosen solution. You plan your algorithm. Technically, this means to write the definition of several functions, methods or classes, which will implement the chosen idea.

Sometimes planning of the algorithm is done together with its implementation, and there is no clear separation between the stages of algorithm design and algorithm implementation.

Once you have a clearly defined algorithm, you implement it. This means writing code to execute the planned steps. In software development, the implementation process includes also testing and debugging.

The last stage of problem solving is to review the results or test the solution with different input data and conditions. For software problems and apps, you need to perform testing of the code, feature by feature: to check for usual and unusual input data and conditions, check for edge cases and special cases.