There are several threads that show various vivs / cages. A search on it (above) will give you some great ideas.
As far as size goes - I have my yearling in a 15 gal aquarium and will move her up to a 20 gal in the next 6 months. Most of mine are hatchlings and are in a rack system in sterilte shoe boxes (Tub Size....14½Lx8Wx4¼H) and will move up to larger boxes (23½x17x6 = 32qt) as they get older.
In the cage you will need :
1) a substrate material like aspen shavings (my choice) or, newspaper, paper towel, repti-bark ect...( you can search on 'substrate' for additional info. )
2) a heat source --like a heat lamp or under tank heater. One side of the tank/viv should be warmer with the substrate in the 83-86 degree (f) range --needed to help them digest their food. The other side should be cooler with temps in the 72-76 degree range. (If you chose the UTH you'll need at thermostat to regulate the temps - when I set mine up without it the substrate in the warm side got to 110 degrees - ouch.)
3) a digital thermometer with a probe - (I got a cheap one at Wal-Mart for $6.00 and it works well). Put the probe in the substrate on the warm side to keep an eye on the actual temp at 'snake level'.
4) A water dish
5) A hide - preferably 2, one on the warm side and one on the cool side - to allow the snake to feel secure and be able to choose.
6) A corn snake
These items can be as simple or as complex as you wish, but will take care of the snakes basic needs. I think that's everything...I'm sure others will respond as well.
I hope this help!
Also - I really enjoyed Kathy Love's Book - Corn Snakes - The Comprehensive Owner's Manual - it, and the forum here gave me all the information I needed to get started and are a great! Here is the link:
www.cornutopia.com - just click on the Books area.