My wife and I climbed Whitney in a day. We are not hikers/climbers and did this because it sounded interesting and we were in decent shape getting ready for our wedding. We walked everywhere we went for 5 months to get used to really long walks, like 2-4 hour walks, home from the bars, dinner, to and from friends houses, etc.
All of our training was at sea level though and pretty flat but better than nothing. Altitude sickness could have bitten us but we got lucky.
We carried very little and did it in trail running shoes with minimal gear. Water, some food, good backpacks, rain coats and hats, one tiny flashlight and a swiss army knife.
We left the hotel at 3 am, Started hiking by 4 and it took 8 hrs. to get up and 6 to get down. The trail is great, nothing technical, lots of people on it (though few do it in a day). We were very VERY sore the next day, could barely walk. Beer and a hottub that night were never so well earned!