Make sure you have a GOOD thermometer. Most use the "indoor/outdoor" ones because they have a probe that allows you to get the true surface temp. (you put the probe right on the substrate over the UTH) That is what really matters since they get most of their heat through their bellies. Give your snake lots of options. in a 10 gal, have at leas two hides, one hide on the warm and one on the cool sides (all heating devices should be on the same end of the viv).
Remember not to feed inside the viv, always in a separate container. This prevents problems due to ingestion of substrate and may or may not help 'train' the snake not to strike when you go to pick it up.
Hides should be relatively small and not too tall. They like enclosed spaces because it makes them feel secure.
Let it settle in to it's new home for AT THE VERY LEAST 4 days, preferably a week or a bit more before you handle, feed, or make too much of a commotion outside the tank. Then, you can start feeding every 4-6 days and, well, you have plenty of time to figure out where to go from there

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Remember that temps should drop 5-10 degrees overnight and that corns are most active during dawn and dusk, so give it some time of partial light, don't just turn the lights off to pitch-black at night. Enjoy your new favorite pet and and the real experts will arrive soon
Addition: The effectiveness of a UTH will be partially determined by the substrate you use as well. Lighter substrate means more trapped air, which means a better insulator leading to less heat getting to the top. A thicker layer of substrate will also decrease the effectiveness. As was mentioned, UTH's make the glass they are mounted on HOT, so put down either paper towels (the cheap way) or $5.00 fake grass mat directly on the glass, then pour the substrate over it. Because they are cold blooded, they can't tell if any single part of their body is too hot, they only know their overall temp. This means that a snake can give itself SERIOUS and possibly fatal skin burns if it has access to any extremely hot surface. This is unlikely with a UTH, but it is all too common with a heat lamp or with a "heat rock." so if you do use a lamp, hang it well above the top. Also. make sure your top is TOTALLY secure. I have 4 metal clips on mine that have a spring-action to hold the lid on tight. These animals can escape like anything. I would reccomend searching Google.com and this site for general corn snake care tips. If you want a single source of info. buy Cathy Love's book The Corn Snake Manual. About 50% of the sites about corns on the internet blatantly plagurize it and it dosen't have anything that you won't turn up after the weeks of research I did online before I bought my snake, but it is a good place to get all the basics from without any of the hastle.
Wow, with this being my longest post ever, I'm sure it is full of errors, but it's past midnight, so I am going to bed, others can fix the problems here. It dosen't look like you are around right now anyway.