Without considering the big picture, it's tempting to dive in and address the direct problem. Surely, that's all that's called for addressing a minor issue with onboarding. You could just move onboarding material to the main page of the LMS. But what if this piece of feedback has popped up a handful of times already?
1. Empathize
The first step calls for you to think of the user. Consider the ways they look for training content. Search around for it yourself. This is where you apply critical thinking to grasp the scope and scale of the problem at hand.
Maybe the real issue is that the content in your LMS isn't well organized and easily searchable. In that case, moving onboarding material to the main page might just solve one problem only to create another.
2. Define
If you're lucky enough to have a team around you, this is a place to loop them in. Take your research and conclusion from the first step. Try to sum it up in a single succinct sentence. Run it by others to see if it makes sense.
After all, you're resolving an issue, not blindly running through a checklist.
3. Ideate
Once you have a firm grasp on the true challenge, it's time to figure out solutions. Brainstorm and toss around your wildest ideas. You don't have to use post-its if you don't want to.
Doing a quick technology review helps ensure you don't miss anything glaringly obvious. Ask yourself if anything has changed in the LMS or in the training program lately.
4. Prototype
Develop a prototype that can work as proof of concept. A common misconception is that you have to go the whole hog on the first fix you come across. Not so. Try boiling a big-picture solution down to something that doesn't require a budget or additional approval. Maybe start with an explainer video.
Whatever you think might work, give it a shot. The idea here is that you're figuring out how to test the viability of a new idea, see if a change is really necessary and, if so, how much of one.
5. Test
The final and perhaps most important step. Run your ideas through the wringer. Encourage beta users to give feedback. Be sure to listen and incorporate that feedback. Acknowledge users when their feedback results in a change to the system or prototype. It builds community and gives everyone a sense that they're pulling together in the same direction.
This is important because you're running through new ideas that don't have a reservoir of data showing their effectiveness. Keep the sage words of David Kelley, founder of Stanford University's design school, known by its whimsical named 'school,' in mind: you have to fail fast if you want to succeed sooner.
Once you have proof of concept for a given idea, restart this whole process and scale it up. If that sounds hard, that's because critical thinking and problem-solving are hard.