It took me ages to find this link for you.
http://support.apple.com/kb/ht1643
Unplug all cables and turn off iPhone (press and hold the Sleep/Wake button and slide the onscreen red slider). Then use the included cleaning cloth or a soft, slightly damp, lint-free cloth. Avoid getting moisture in openings.
Don't use window cleaners, household cleaners, aerosol sprays, solvents, alcohol, ammonia, or abrasives to clean iPhone.
Another support article recommends you use iKlear products (apparently its the only product they use at Apple Stores to clean iPhones and macs). Should you use that product you bought? I don't know... I'm just giving you more information.
Extra: Do not use isopropyl alcohol on the bare LCD panel. Use only a damp, soft, lint-free cloth or LCD cleaning product like iKlear.
http://support.apple.com/kb/HT3226 <-- How to clean Mac products