not sure if you are doing a kit or going from scratch, but all i can say is, sanitize everything. it's just like making beer if you've ever done that.
also, make sure you aerate (ie stir-- don't need any fancy equipment other than a spoon) the wine/water mixture. you kinda wanna "whip it" so you get nice bubbles on top. basically the idea is to get O2 into the solution so that the yeast can "take off"!!!
another thing, i'd recommend keeping you ambient temp 80 or less. 78 or less if possible. we're entering the cooler seasons now, so that shouldn't be a problem. don't allow too many temp fluctuations-- stick it in a back closet, or somwhere the temp doesn't change.
the kits are pretty much foolproof. i'm on my third one now, and the first two came out great!
i respectfully disagree w/ the hydrometer for 2 reasons.
i've never had good results (maybe i'm just an idiot)
and once you drop that thing in a carboy, you can't get it out, and if you decide to de-gas with a power drill and stirring rod, you're likely to destroy it, leaving all kinds of fragments in your nice expensive kit
plus, if you're doing it in your primary (assuming it's an opaque bucket) you'll have to pop the lid everytime and run the risk of contamination.
look, if you're running 72+ degrees, and you let it sit about 10 days in your primary (assuming you had a good liftoff) and then you transfer to a secondary carboy (take some of the sediment with you) and let that sit for however long you want (at least a couple of weeks), it's VERY hard to imagine you have much fermentation activity going on at that point.
Well I don't like to disagree with somebody I haven't met.
1) Don't drop the hydrometer in a carboy. For one thing it's hard to read there. Use a Fermtech Wine Thief (see http://www.fermtech.on.ca/thief/thief.html) or a hydrometer tube (comes with most equipment starter kits)
2) I wouldn't worry about contamination in the primary because of the CO2 & SO2 being generated by the fermentation. If the ferementation is slowed then the sg should show that it is time to transfer to carboy. Plus I don't check every day. I wait until the 7th day.
You can even use a turkey baster and a deep measuring cup if you don't have a wine thief or test jar available. Just sanitize the measuring cup and baster and hydrometer. CPFan is correct though, a valid hydrometer reading is the proper way to ensure a complete fermentation.