Not sure whether this answers the OP, but yes you can manually enter coordinates (if you really want to!)... Press the 'FIND' button, and 'Coordinates' is one of the options.
I think the advertising blurb you quoted was to do with 'paperless geocaching', where there is no need to resort to using the above metod.
To see paperless geocaching in action, connect your 62S to your PC and go to http://garmin.com/geocache
To see the 'paperless' part (once you have downloaded one from the above site), press the 'FIND' button, then 'Geocaches'. select a cache, press 'ENTER' to see the map location, then 'MENU' and select 'Review Point' to see the instructions (though not the hints - you can get those from the web if you need them).
You also ask how you can see what coordinates you are at... You can add that field to your map screen if you like... First, from Main Menu/Setup/Map, choose '4 Small' (for example) in the 'Data Fields' box.
Now PAGE (or QUIT!) to the Map screen, where you will see the 4 small data fields you asked for! To customise them, press 'MENU' while in the Map screen. Then select 'Change Data Fields'... Select on of the 4 (it will turn blue)... One of the many options is 'Location' - this will show your current coordinates, in whatever format you have chosen when you setup your map. I use the British Ordnance Survey Grid, for example. Useless if you're not in UK!
Hope this helps somewhat.