There are modules that exists (Drupal-to-Drupal data migration, Data Export, Migrate), however the more customized your original Drupal 6 site is, the harder it becomes to easily transfer data.
I would try with some of these modules and see how they perform based on your exact scenario - you may be lucky and it will all work fine.
If it doesn't then you have to take a more manual / custom approach. I've done this before by exporting data from the old site to a csv with a custom script, and then writing another custom script to import the data into the new site. This can handle complex relationships that generic import / export modules can't cope with, but takes longer and requires a more intimate knowledge of how Drupal works.