You registered at NeuroNation with an email address and a password. These are the only two pieces of information you need for a login at www.neuronation.com.
If you are not already logged in, click on the top right icon "Login". A small window will open where you need to enter your e-mail address and your password. If you confirm, then you will be logged in with your user name and it will show in the top right corner of the screen.
If the word "Premium" appears on the top right corner, next to your user name, then you are already logged in and can begin training. To start training, press on "Training" and then select whatever exercise you would like to begin with.