Create the new Aurora RDS Instance
If necessary select your region
Instances > Launch DB Instance
Go through and select your desired set up.
Database Options > Database name: Give the name for your database (if you don't you'll need to add a database later to your instance using a MySQL tool of some sort
RDS Dashboard > Instances . Use the arrow to open up your instance info once its running
Connecting to your Aurora database
If you set your RDS as publicly accessible then you should be able to use these to connect using a standard MySQL tool.
HostName/Ip Address: The 'Cluster Endpoint' with the ":3306" port number removed from the end
Port: The port number that was on the end of the 'Cluster Endpoint'
Username and password: as you set when creating the master user.
If you didn't specify a database name when setting the RDS up you'll need to add your database before then adding your own tables etc to it. By default the Aurora RDS will have a database called "mysql" in it with various tables it uses.
Security Group (Inbound and outbound connection rules)
RDS Dashboard > Instances . Use the arrow to open up your instance info once its running > Details tab on left > Security Groups: You will have the one created or selected when setting up the RDS. Click on it to go edit it etc.
In our test the default security group had already got a default inbound rule for our PC that was setting up the RDS to be allowed to connect (our desktop MySQL editor tool was able to no problem), but would not allow any other outside IP addresses to connect (when our web server tried it got a connection timeout). To do this all that's needed is to add a new inbound rule for the new IP address. If you get problems you are able to add an inbound rule that allows a connection from anywhere (any port and IP address) which can allow you to prove a connection can be made before then locking it down to a single port and IP address (in our case we discovered our web server was connecting from a different IP (address to the one we'd assumed, somethign we had to work out externally as RDS doesn't appear to log incoming connection IP's).)