When a Contact is created, it'll automatically inherit the address which was created for the Company and Company. However, you're able to change the address to a new one for the Contact if you'd prefer (for example, if this particular Contact works primarily at home).

How do I add a second address to an existing contact?

Simply locate the required Contact and then select the Addresses page on the left-hand side. This will display the current address and will also allow you to add a new one.
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Select 'Add Address' and you'll then be able to search by postcode or street name to locate the required address. 

It'll then automatically populate the address details for you, or you can enter them manually if preferred. Clicking 'Confirm' will save the details. 

This will then display the new address next to the previous Company address. 

If required, you can return to using the Company address simply by clicking on it. You'll then be prompted before the changes are made to check you're happy to confirm these changes.