Government entities generally put work to be done out for bids. This is done through their website or public works departments. Be sure to read the directions very carefully and follow them to the letter. Also, answer each and every part of the bid.

The SBA offers the 8(a) Business Development Program which helps disadvantaged companies compete.
Disadvantaged Business Enterprise Program (DBE) administered through the Ohio Department of Transportation.
The U.S. Government uses the System for Award Management to certify contractors for bidding.
The U.S. Government uses FebBizOpps.Gov to manage contract awards. You must be listed in the SAM system prior to bidding.
SBA Certification Information
Finding opportunities with the State of Ohio
Additional information on selling to the State of Ohio
The Kent Procurement Technical Assistance Center (PTAC) helps in all areas of government contracting.
Small Business Development Centers at The Summit Medina Business Alliance.