A typical Oracle database is 1 TB or more in size. This will mean that a T3 line or higher speed line will be needed to move this much data. Otherwise, the AWS import export service can be used. The information below is from the http://aws.amazon.com/importexport/ web page but repeated here for easy of finding.
Connection Theoretical 80% Utilization AWS Imp/Exp
T1 (1.544Mb) 82 days 100GB or more
10Mbps 13 days 600GB or more
T3 (44.736Mbps) 3 days 2TB or more
100Mbps 1 to 2 days 5TB or more
1000Mbps Less than 1 day 60TB or more
Elapsed time is going to depend on many factors: speed of connection, compression used (if any), can load be done in parallel etc. The fastest load times will happen using AWS import/export (http://aws.amazon.com/importexport/ ). The next fastest will be using AWS Direct Connect (http://aws.amazon.com/directconnect).
Direct Connect provides speeds of 1 Gbps to 10 Gbps. Using a 1 Gbps line, it would take about 3-4 hours (here is a good site: http://fasterdata.es.net/fasterdata-home/requirements-and-expectations/).