The SketchClub app automatically remembers your account so you don't have to remember any passwords or things like that. If you switch to another iPad or iPhone and want to use your account there you need to use one of the Account Recovery options.
When you edit your profile info you'll see an option for a recovery email address. Put your email address here and it'll make returning to your account on other iOS devices very easy. The email address will be used only for account recovery.
When you start on your other device you'll be in a temporary Anonymous account. Go to the profile page for it and you'll see a link to "Recover Account". Tap that to get a field where you can enter your recovery email. An email will be sent with a link which you simply click to allow that new device access to your account.
If you've linked your account to Google or Facebook it's easy to access it from another device - just login!
To return to an account that had no recovery email address set for it and was not linked to Google or Facebook the last resort is getting help via support@sketchclub.com. Please include a link to your old account's profile and your new account's profile.