Before you can begin the building process, you must obtain a building permit. Check with your building department for requirements. Also check how long the process takes. Generally a building permit takes between 2-6 weeks to obtain once the building department has all the necessary documentation. The building department may require many of the following: 2 complete sets of plans, engineering specs, MECcheck (Model energy code check), truss details, drainage plan, permit fee, etc.
A variance is a exemption from the zoning committee to exempt your project from certain building zoning or building regulation. For example, a common variance that is sought is the building setback. Zoning and building regulations require that a building is "setback" a certain distance from property lines. If you want to place your home closer than the current zoning regulations, you will need to apply for a variance.