This is a big problem when the access is from different geographies.
RDS off late has some support for cross-region "read" replicas. Take a look here. http://aws.amazon.com/about-aws/whats-new/2013/11/26/announcing-point-and-click-database-replication-across-aws-regions-for-amazon-rds-for-mysql/
Dynamo DB doesn't have this. You might have to think of partitioning your data (keep Asia data in Asia and US data in US). Another possibility is to increase the speed by using an in-memory cache. Don't access Dynamo DB always for all the reads: After every successful read, cache the object in AWS Elasticache - setup this cache to be near the required regions (you will need multiple cache clusters). Then all the reads will be fast (since they are now region local). When the data changes (write) then invalidate the object in the cache as well.
However this methods only speeds up the reads (but not writes). Typically most apps will be OK with this.