Shrey, this is all covered in the online documentation, so you should read through this topic to gain a broader understanding of working with AutoCAD files.
Having said that, the import is pretty straight forward.
You start by going to Open File... and changign the filetype to DWG. Then navigate to your file and open it
You'll be presented with the DWG import wizard. You want to set the wizard to import your DWG as 3D Curves and models into a part. (If you want to import the dwg as an assembly then open it in draftsight and export it to an ACIS .sat file and import that into SolidWorks)
Click Finish and the 3D Solids will be converted into solid bodies in a part file. In your case, there were some geometry errors on the import. Usually these crop up at the intersections of two faces. In this case, since the body with the errors is a duplicate of another body, I'd delete the offending geomtry and use the move-copy bodies tool to clone the good piece.