Methods of nuclear transfection - nuclear transport
My attempt to find an answer has suggested that no-one knows how the DNA gets into the nucleus.

This fairly recent paper reports attempts to track the pathway of DNA entry and transfer to the nucleus.


  Le Bihan et al. (2010) Probing the in vitro mechanism of action of cationic lipid/DNA lipoplexes at a nanometric scale. Nucl. Acids Res. 39:1595-1609


The technique used was transmission electron microscopy. Complexes of plasmid DNA + cationic lipids (lipoplexes) were labelled with silica-based nanoparticles to allow visualization.

The authors describe a transfection pathway with five steps:


  (i) binding of the lipoplexes to the cell surface; 
  (ii) entry of the lipoplexes into the cells mainly via endocytosis (a direct fusion with cell membrane cannot be excluded); 
  (iii) DNA release into the cytosol;
  (iv) transport through the cytosol; and 
  (v) entry of DNA into the nucleus and nuclear transcription.


The authors were able to follow each of the first four steps but:


  our data show nanoparticles close to, but not within, the nucleus.


They speculate about what this might mean, but they do not refer to any previously published data. My conclusion is that the answer to your question is, as I said at the beginning of my answer: no-one knows how the transfected DNA enters the nucleus.