How can I install this automatic transfer switch?
According to the Manufacturers Installation Guide (PDF)...

Physical - install the UTS within one foot of the building circuit breaker panel

Page 4

Caution: The UTS must be installed within one foot of the building circuit breaker panel. If the UTS must be located further than one foot from the circuit breaker panel, a licensed electrician must extend the wiring using standard electrical wiring conduit and junction boxes.

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According to National Electrical Code (NEC)...

National Electrical Code 2011
ARTICLE 110 Requirements for Electrical Installations
110.3 Examination, Identification, Installation, and Use of Equipment.
(B) Installation and Use. Listed or labeled equipment shall be installed and used in accordance with any instructions included in the listing or labeling.

I'm guessing the unit has permanently attached wires in a raceway, which is of a limited length.  So mounting the unit further from the panel would require you to extend these wires and raceway, which requires knowledge of wiring methods to do properly.  It's not likely you'll have to upsize the wires, but you will have to understand basic wiring methods (Chapter 1-4 of NEC).