Peter,
As Cyber and chuk rightly advised, using your finger(s) and thumb(s) is how a smartphone screen is used. It is therefore called a touch screen, and requires only light touches.
If your touch screen is not responding to light touches, and is less than 15 days old, you may want to return it to the vendor. You may first want to check with the vendor to see how many minutes of calling, etc. that it experienced to still be returnable.
If it is beyond 15 days old but less than one year, and has not been abused, which includes deep scratches on the back plate or water damage, it may still be under warranty. Before having it sent in for repair, do a hard factory reset. This is a measure of last resort, as EVERYTHING will be deleted from the phone subsequent to the day that it was purchased brand-new. As a result, back up everything that is important to you, such as photos, phone contacts, videos, documents, etc.
If the factory reset does not resolve the unresponsiveness of the touch screen, it's time for repair, if under warranty, or the purchase of a new phone.
Good luck!