There are several methods better than an auto-drip machine for brewing your coffee, ranging from inexpensive pour-over's like those made by Melitta, to the more expensive French Press or Chemex. There are also, of course, many other brewing methods, but I've found these to be the easiest for beginners.
Water is an incredibly important part of brewing coffee. I highly recommend using a water filter on your faucet or one of those filter containers that you can stick in your refrigerator. Quality water makes quality coffee. The water temperature should be between 195-202 degrees but 198-200 degrees is optimal in most cases. If you want to get technical you could grab a thermometer and check the temperature of your water but if you don't have one you can let the water boil and then let it sit for about 30 seconds to a minute so that it can come back down to roughly the correct temperature range. Alternatively you can pour it from your hot water kettle into another vessel to drop the temperature sufficiently. Just make sure not to use boiling water when making your coffee because it will over-extract.