From Windows with Putty
Download putty and puttygen.exe at https://www.putty.org/
Open puttygen.exe and load your key pair with .perm extension. You must have this file. It was generated when the instance was created.
Then save it as private key with .ppk extension:
Open putty.exe
Go to Connection / SSH / Auth and browse the private key:

Go to ECS instance in AWS Console and copy the DNS address:
Paste on putty, and save it if you want. Then click on open:
Enter ec2-user (this is the default but you can change it) on the login.
How to connect to AWS EC2 instance from local