Magento v1 uses oAuth 1.0 and has some limitations so it is recommended to use Magento 2.0 if possible.
To connect use the webiste Admin => oAuth 1.0 page to do your oAuth 1.0 authentication.
Your base URL will be like <magento_url>/shop/default
You will need to log into Magento as Administrator and go to System => Webservices
Please create a Rest Roles, Rest Attributes, and a Rest Consumer.
The Rest consumer will give you the Consumer Key and Secret which you need to enter below, then click the Authorise button which will make you log in to Magento, then return you to this page with the Access Token, Verifier, and Token Secret populated.
Once you have done you Authorisation then copy the Consumer Key, Consumer Secret , Access Token, and Token Secret
Open up the Magento Retailer and go to the API section and fill in as outlined
Note, due to paging issues in Magento 1.0 you need to include the entity_id filter as shown below. Also the Last Downloaded field represents <months prior to search>:<lowest search date> as there is no updated_at field available.