I cannot find a battery replacement for my Kenneth Cole watch KC4584. It says on the back, C275-07 for the battery.

They all set pretty much the same. Here is the general walk through from the Cole site:
Press the lower left button on the Kenneth Cole digital watches to cycle through the various modes. Press it three times to get into time mode (the face should be blinking). Press the upper right-hand button to change the seconds. Press the lower right-hand button to select the minutes.

I could not locate a manual or instruction guide using the internet search of https://www.google.com

I did see a battery replacement video and source for a battery, as many questions on FIXYA are from people who don't seem to want to go to a watch repair or jeweler to replace a battery.

https://www.youtube.com/watch?v=VOkR-IKaOic


How to Install Battery on Kenneth Cole Watch


https://www.bigapplewatch.com/battery.asp?prod=battery&watchnumber=Kenneth%20Cole%20KC1502

Remove back of watch small pearing knife will do careful silde under back to remove battery

i am not understanding ......

you need Manuel for replacing battery ?

or

you need Manuel for setting up digital part of your watch ?

Definitely yes, unless you've got some cheap copy.

I suggest you contact the maker by going to their web site http://www.genevawatchgroup.com/ (this is the maker) and speaking to them. You are not the first to have this kind of problem and they should be able to sort it out for you.

Open watch case back, then release the metal contact covering the battery. Memorize battery's polarity (+ up and - down), then take the battery out. Memorize the combination of letters and numbers on battery (should be something like: CR 3216 or similar). Make does not matter - Seiko is as good as Maxell, Panasonic and other reputable makes. Buy new battery with identical combination of letters and numbers and put in your watch. Replace back contact, gasket and case back. Set your watch and enjoy. Rate me, please.

Get a flathead screwdriver from eyeglass kit and the back cover will pry off to replace battery