In short, it depends on a deep understanding of the problem, so before you go through any further, learn what is your problem all about.
The following steps are best suited for innovative businesses, large corporations, or government bodies, where you usually have complex problems that cannot be tackled directly.
Scope and Knowledge
In order to succeed you need focus. State your priories ahead. Complex problems tend to drag the process into many different avenues and you cannot solve all related problems in one go. Also chose wisely based on target goals (e.g. target KPIs), not every seemingly important problem is actually important.
Write down all what you came to know about the problem, based on research and observations. State every thing in a systematic manner, so you can refer back to it. Use a lot of useful sub-titles.
Identify the Challenge
According to the scope, you are focused on a specific area. Identify the main challenge within that area. Also choose a challenge that can be feasibly solved. Between changing the height of a short chair and that of a tall person, it is often clear which challenges can be feasibly solved.
Know the Cause. You can use the popular and simple fish bone diagram to connect your causes to the effects (Cause-Effect diagram, also known as Fish Bone diagram) if you have only one root effect. If however, the problem is complex you can use a more detailed root cause analysis to highlight root causes and identify solution direction.
Find and Implement Solutions
Based on the root cause analysis, select the best solution within the project scope. Depending on the complexity you can use something as simple as group brainstorming or you can go for the more advanced TRIZ 40 principles.
Validate your chosen solutions against set goals and more importantly relevant intellectual property and prior art. Ideally this can be done in parallel with your solution generation efforts.
After solutions are vetted, you should have one or two solutions that have high conformity to set goals, and are also very feasible to implement.
The winning solution must be optimized to match implementation methodology. For example: if the solution is a mass produced product, it would require design for manufacturing optimization.
The final step is implementing the solution you have worked hard on. Different problems have different implementation methodologies, however they all require one thing Taking Action.
Alternatively, your organization can simply acquire an existing solutions or start-ups that have already solved the same problem.