Every field is a little bit different, but here are a few things that I've done in the past that have been helpful. If I had to boil it down - and this may seem obvious - but study the field as intensely as you can; and surround yourself with people in that profession. Most of all...be patient and enjoy the experience along the way. Becoming an expert in any field can take years of hard work. Good luck!
Unless you are majoring in a very specific degree - make sure you learn as much about the field as possible before looking for jobs. I know that can be a challenge when you already have a full school schedule. But the more you know, the more you'll stand out from your peers and the less you'll be surprised by the expectations or job requirements once you start.
Leverage your network. If you know people in the field already - they can be your best asset. Make sure they know your interest (don't assume). Talk to those people and find out specifically the steps they took that made them successful. If you can have one of them serve as a mentor - even better. If you don't already have a network in the field - things like alumni associations, local professional organizations (specific to that field), or LinkedIn groups can all be a great starting point.
And when you do look for a job - Be willing to start at the bottom and work your way up. Look for companies that inspire you - even if the first role is not exactly aligned with your dream job. You'll be surrounded by people that are where you want to be and you'll see how they work first hand. Take on extra projects and assignments as often as possible. That's the path I followed and it's resulted in a great career working with people I enjoy and admire.