Having used AWS for a few years, there are numerous ways to get "your data" to the cloud. Usually the simplest is export/import (bias towards Oracle), but this process is usually slow when you start moving large data sets. There is the RMAN backup/recovery manager but this requires you to have the same instance version in the cloud - not good if you want to upgrade at the same time. Datapump is also available and is very useful as you can do Network data Pumps across database links - but again this can sometimes be slow.
I then looked into using Amazon's Advanced Data Migration Techniques (published Nov 13 2013) and decided to give it a go and have posted my walk through below (quite technical):
This was done from a local "data center" 100GB database, exported using datapump, copied to a M1.Xlarge EC2 in cloud and then copied further to the backend DATA_PUMP_DIR on the RDS instance (which you don't have access to). Then a datapump import into the RDS and job done - took me approx 12 hours in total (and that wasn't using Tsunami).