These tips from Forbes are spot on. Two of my favorites:
Gain the boss’s trust by mastering the little stuff.
When you’re first starting out, not only are you young and lacking much work experience, you’re also new to a company and team of people. You have to give your managers a reason to trust you. You probably won’t get big projects or responsibilities in the beginning—but if you treat each small assignment with the utmost importance and pay attention to the details, your supervisor will gain confidence in your abilities. When I first started, I tried to nail every little project. Fact-checking? Just you wait while I lay down some accuracy. A 100-word blurb? Those will be the best 100 words you’ll ever read!
Raise your hand for the bigger stuff.
Once you’ve proven you’re reliable, aim for more challenging projects or positions. Usually, these things don’t just happen. You have to ask. I raised my hand by volunteering to take things off my editors’ plates, pitching stories that were important to me and asking to be put on projects that I could learn from. It’s not all external, either. I also pushed myself to delve into topics or situations that were scary in the short-term but good for my career.