ED is hard to enter without experience in a related field. The problem is that outside of a few large cities, most ED organizations are small operations. The staff is called upon to have broad, detailed knowledge, and especially, ties to the targeted communities (i.e., developers, site selection consultants, etc.). When I tried breaking in, I kept seeing every job listed with a requirement for a masters degree and 2-5 years of experience.
There are good ways to get in. As a planner, you might develop a specialization in redevelopment. As a public administrator, you might look at local or state agency jobs in CDBG administration or grant program administration. As a business major you could look to demographic (market) analysis or international trade.
One technique to start a career directly in economic development is to look for small communities or small programs. Main Street programs are an excellent opportunity to develop the skills for an economic development career, but be sure to network not just with other downtown developers, but also with the broader economic development profession.
After the Army I snuck into economic development in a small rural community, working part time during grad school. They cold not afford more, and I were happy to get somebody with an educational background in the firld. After a year in retail site selection I plotted a return to the field, and landed a job in another rural community. Over the next two years I was active in several organizations, built a good network, and was recommended for my current job by my predecessor before he left.