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I have a CAD file of a building and I want it to be replaced on Google Maps with coordinates.

The DXF-file is on a local coordinate system (undefined). I convert this file to SHP-file for editing. I have corner coordinates from Google Maps. I want to determine the WGS84 coordinates for this SHP-file.

Should i use the affine transformation method (what are the parameters?) or other method for ArcGIS?

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In ArcGIS you should load the CAD data first and use the Georeferencing toolbar to establish world file coordinates before converting to a shapefile as explained in the Georeferencing CAD datasets help. There are several related help links in this section that explain how you can apply a transformation, but that generally means that the local coordinates had to apply the rules of a known projection to choose the appropriate transformation. In most cases a decent set of control points on a horizontal or vertical plane should be sufficient for placement and sizing of a single building footprint.

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