This is a great question and something I have been thinking a lot about. Especially in how to teach this skill online vs a classroom setting.
If I had to pick four important factors to becoming a good designer they would be.
Pencil sketch before moving to the computer
Sketch a lot of thumbnails with paper and pencil BEFORE working on the computer. A gradient or cool font will never save a poor concept. This is the discipline required to achieve high quality concepts and solutions.
Emulate the work and design style of professionals
Emulate the work and design style of professionals. Look at work you see on large sites, design awards, magazines, and books. You should strive for your work to be just as good.
Learn art history and past graphic designers work
Learn art history and past graphic designers work. You will see themes and patterns you can use in your work. Colors, lighting, composition, etc.
Have a reason for every design element
If someone asks you “Why did you use that picture or that font?” “What is your reasoning for having the navbar behave like this?” Since you spent a lot of time on the strategy and sketching, your design should have reasons for every element and support your goals. If not, consider removing it. Sometimes the best addition is subtraction : )
Be aware of design trends but don’t abuse them
Sometimes designers have to follow design trends because that is what the client wants. You also don’t want to appear out of touch and dated.
So I recommend being aware of trends but don’t gravitate to them just because they are cool. Focus on sketching and thinking way more than the visual aesthetics. If the design trend is appropriate for your design solution and will support it then use it. If not, really question if it makes sense to use it.
Embrace the design process
The majority of what we do is organization of content and helping people communicate or use an application/tool.
Have frequent group critiques guided by a professional
Have frequent group critiques guided by a professional. This will help you hear questions like “Have you tried x?” “What more can you do?” Outside opinion is really important in helping you see things differently.