More detail
AWS handles installation, patching and backups. You still connect the normal way, with a database username and password over the network (port 3306 for MySQL). RDS runs inside your VPC, so security groups decide who can reach it.
RDS goes into a DB subnet group: a list of private subnets it may use. The group must cover at least two Availability Zones, even for a single-AZ database, so that a standby can be added later.