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Any more, it's all on the computer - AutoCAD is the most common drafting app you'll encounter, but Revit , which is 3d model-based, is advancing quickly. Most likely you'll start out transferringing someone else's pencil-and-paper design to the computer.
Start with a CAD class at a community college or technical school. There's also something to be said for studying the basics of plan drafting - things like dimensioning and shape description are common to manual drafting as well as CAD.