Barn demolition and deconstruction are relatively straightforward due to the simple nature of barns. Because of this, it isn't uncommon for owners to consider the project DIY-able. However, just because you can do the work, doesn't necessarily mean you should do the work.
Hire a professional who can handle the project properly and efficiently. Truly reputable barn removal contractors should have insurance and references from other customers who can attest to their ability to complete the work.
Comparing 2 - 3 contractors (or more) will help make sure you find the right contractor without overpaying. Discuss with each one who would be responsible for cleaning up the debris, whether or not they would collect the permits required to perform the work, and what would be included in the price. Getting quotes from multiple contractors will make sure you make the right choice.