@Hannah Lucas - Interesting deal you are trying to solve. The first step is to pull up the municipal zoning, and determine which zoning district the lot is located. Once you know that, you then research that district to determine the minimum lot requirements for subdividing a lot. Each municipality has their own zoning, and there are usually quite a few diffierent residential districts within a community. Having the existing survey is also a requirement to determine if what you intend is possible, because it will show where the house is located on the lot. That will impact potential setbacks for the new yards.
If you can't find this information or have questions, the municipal planner and/or a local architect should be able to assist you - assuming you have the survey.
Complete new builds are slightly different than a tear down. You willl most likely have to go through the subdivision process in the municipality, which requires survey of subdivision, new legal descriptions and PIN numbers. Most municipalities have a committee to approve this process typically known as the Zoning Board or Plan Commission. There may be an impact fee for the schools, etc.
Once you have those approvals, then you will still need to submit for building permits. There are nuansces depending on if they property is supported by local utilities or wells/septic are required. If you have not retained an architect, you will at this stage. Getting a GC on board will also assist the process. In addition to @Scott E. list of vendors you will also need an attorney to assist you in preparation of the subdivision.