How can I reset my iPad without an iCloud account?

Presumably, having reset the iPad, it is now Activation Locked...

Activation Lock

Here are the Apple support pages that outline the Activation Lock - and the only mechanisms by which it can be satisfied:

Activation Lock for iPhone, iPad, and iPod touch - Apple Support

Turn off Activation Lock – Apple Support

As you will discover, unless you are the owner of the AppleID that was last used to activate the device, you’ll not be able to defeat or bypass the Activation Lock. With documentary evidence that you are the original owner (such as sales receipt showing the serial number), Apple may be prepared to assist - otherwise they and nobody here will be able to help you.

If you have the necessary documentation, Apple have recently introduced a new portal though which you may be able to request release of an Activation Lock:

How to remove Activation Lock - Apple Support & start an Activation Lock support request.

AppleID

You may also need your AppleID and associated password. If these have also been forgotten, they can be recovered here:

https://iforgot.apple.com

To recover your credentials, you’ll need access to one of the following:

• Your primary email address mailbox that corresponds with your AppleID
• Any of the secondary/recovery email addresses that should be configured for your AppleID account
• Any of the trusted telephone numbers (fixed line or Cellular/Mobile) that are associated with your AppleID

More information about recovery of your AppleID and associated Password:

If you forgot your Apple ID - Apple Support

If you forgot your Apple ID password - Apple Support

MichaelB10 wrote:

If you completely reset the iPad and it shows the screen with “hello” on it, then you can set it up like you do when you get a new iPad. Click here for more information.

Resetting the iPad will show the hello screen, but it is step 4 that will display the Activation Lock if the iPad is locked to the original owner. This step requires an internet connection to contact Apple servers to verify if the iPad can be activated. They will need the credentials for the Apple ID that the iPad is locked to or the original purchases receipt to remove the Activation Lock.

For security, the "clue" intentionally doesn't reveal the full email address or phone number. Suppressed characters are replaced one-for-one with a dot/asterisk.

As already outlined, information about recovery of your AppleID and associated Password can be found here:

If you forgot your Apple ID - Apple Support

If you forgot your Apple ID password - Apple Support

The iPad is Activation Locked. You're seeing a clue to the AppleID that was last used, by you, to activate the iPad.

If you have forgotten the AppleID credentials, you'll need to recover them using the guidance already provided.

If you have changed your details, you are running out of options. Unless you can recover the AppleID credentials, without Apple's assistance, the device will be permanently beyond use.

Presumably you are using different AppleID accounts for both your old and new iPads. If you were using the same AppleID for all your Apple devices (as is recommended), you would be in a much better position.

If you completely reset the iPad and it shows the screen with “hello” on it, then you can set it up like you do when you get a new iPad. Click here for more information.