Is there an easy way to move user data between 2 sites? I am totally new in Drupal, and I am using Drupal 7. I was asked to move data between two sites that don't even have the same structure, and have different fields. 

Can anything bei done with a tool like Drush, or with MySQL?
You could possibly use views to output the data you want into a csv file (with views data export module) and then import the data into the destination site using Feeds module. This technique has worked well for me on a number of occasions. 

Additionally, you could try the Features module but this is quite complicated and may be difficult to get your head around initially.