Through assimilation and autonomy. The Frank's who migrated into modern day France had successfully Romanized to a degree that Charles the Great was crowned Augustus by the Pope. Likewise, the Ostrogoths in Italy adopted many Roman-Italian customs and mostly kept to themselves in the north.

Another common trait was that they controlled the military. Germanic conquerors often comprised their armies of their own countrymen to prevent the locals from getting too strong. For the most part, the peasantry didn't care who their overlords were as long as they were given autonomy and weren't taxed too heavily. Not having to die for some king's war was a bonus.