I bought an apple watch and the previous owner of the watch has not removed it from their phone. I can not get in contact with them, how can I activate it if I do not have their apple ID or password?

Click on this link to read "About Activation Lock on your Apple Watch" --> https://support.apple.com/HT205009

For an individual to remove an activation lock absolutely requires the information for the account that applied the lock. Click on this link to learn 'How to remove Activation Lock' --> https://support.apple.com/HT201441

If you do not know the required information and you are not the original owner, get the owner of the account to remove the lock or return the device for a refund or recycle it. The device is otherwise useless to you. If the owner is unknown and has not provided contact information as a message showing in the login screen, there is no way to contact the owner unless the person who gave you the device knows them.