Second to yeast (and sugar), sanitizer is probably the most important item to have when making wine or beer.  Every piece of equipment that comes in contact with your wine or beer must be washed and sanitized.  Bacteria is everywhere and all it takes is one to spoil a batch of homebrew.  Simply do a Google search for "pruno" if you need more descriptive reassurance.  Wash and sanitize all equipment, and wash your hands of course.  There are several sanitizing solutions available; here are the ones I've tried:

Potassium Metabisulfite

This is the compound found in Campden tablets (and also available in powdered form).  Some winemakers use sulfite because they already have a supply of it on hand and it's going to go in the wine anyway, so it might as well be used for sanitizing as well.  I don't use it for this purpose because Campden tablets have a relatively limited shelf life and it's anyone's guess how effective they are after sitting in the drawer for several months, not to mention it's a hassle to crush and dissolve them due to their low solubility in water.  Be sure not to breathe the dust they create; I did once by accident and was coughing all night.  To create your own solution, crush 16 Campden tablets with a mortar and pestle and dissolve them in one gallon of water.  You might as well dump out the solution when you're done with it because it probably won't be full strength by the next time you use it.

Iodophor is a concentrated no-rinse sanitizer that easily mixes with water.  The guy at the my local home brew supply store swears by it.  Although it has a pungent odor, it reportedly does not create off flavors when used according to the instructions.  It will, however, stain anything it remains in contact with for an extended period of time, especially in its concentrated form.  I've had shitty brown stains on my hands for days as a result of the occasional spill.  It's also turned some of my plastic equipment a slightly brown color, which makes it look dirty even though it's not.

This is my favorite sanitizer.  Star San is a mixture of phosphoric acid and dodecylbenzenesulfonic acid that is harmless in diluted form.  It has a very mild, almost unnoticeable odor and does not stain.  If stirred, it will create thick suds.  At first, I was obsessive about letting all the foam drip off but then, after reading numerous forums giving the advice "don't fear the foam," I learned to stop worrying and love the Star San.  Star San will, in heavier concentrations, peel the fucking skin off your hands, so follow the directions on the bottle.

This method should only be used in the event you absolutely zero access to proper sanitizers which might be the case if you were either in prison or in the midst of a zombie apocalypse.  Boiling water will sanitize equipment but it takes time not only to heat up the water, but also to kill the microbes.  Then you have to find a way to remove your equipment from the boiling water without contaminating it again and without burning yourself in the process.  Just use a real sanitizer.

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Potassium metabisulfite is a necessary preservative for winemaking unless you're trying to make super organic healthy natural vegan wine and want to roll the dice with spontaneous fermentation.  Any fruit you pick yourself or buy from the store will likely be carrying some form of microbes on its surface, which will begin fermenting on its own once you turn your back on it.  Once, I made fresh lemonade from my neighbor's lemon tree and left it in a sealed glass jar.  I forgot about it and opened it a week or two later to find the jar pressurized and the lemonade carbonated, with a white, floating growth on the surface (it tasted alright, incidentally).  However, you can never tell whether the microbes that hitched a ride on your fruit are the kind that make booze or the kind that make the nasty shit that drips out of the bag when you're emptying the kitchen garbage can.  The best precaution is to crush some Campden tablets (one per gallon of wine) and dissolve them in a small amount of water, then stir it thoroughly into the wine.  The potassium metabisulfite will kill bacteria and wild yeast, but will not harm lab-cultured yeast.  Let the sulfite sit in the must for 24 hours before adding the yeast.  This allows some of the sulfite to bind to the sugars in the must.

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Primary Fermenter

A primary fermenter is simply a food-grade bucket.  A glass carboy can also be used but this makes it difficult to stir the contents because of the narrow opening.  Make sure your fermentation bucket is food-grade.  The plastic buckets you find at the hardware store probably contain chloride or some other harmful chemicals that can leach into your product.  Always use a primary that is larger than the volume of wine or beer you plan to make.  This is to ensure plenty of head space at the top, in case the fermentation foams up and starts pushing its way out of the airlock.  For example, even though I'm making a five gallon batch of wine, my primary actually can hold about seven gallons in volume.  Different combinations of fruits, grains, and yeast can create dramatically different fermentation caps, from a few bubbles on the surface to several inches of foam.  Always leave enough space at the top.

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Airlock

Three Piece	S-Shaped

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When fitting an airlock to a carboy or jug, you'll need a rubber stopper to seal it in place.  I'm not a fan of rubber stoppers because they make the neck of a carboy smell like rubber, which I don't want to smell when I take a sniff of my wine as it ages.  Stoppers are also made of silicone, which is odorless.  However, the silicone ones tend to slowly squeeze out, especially if they're wet.  Sometimes they will pop out minutes later, after you've turned your back.  I often secure them with gaffer's tape until they cooperate.

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Racking Cane and Tubing

After fermentation has finished and sediment accumulates on the bottom, a racking cane, or auto-siphon, is used to draw wine or beer from one carboy to another, leaving the sediment behind.  This process, known as racking, results in a clearer liquid each time.  Some "learn to brew" kits, in the interest of simplification or cost cutting, only come with a tube and expect the user to initiate the flow using one's mouth or with the assistance of graviy.  Don't be a cheapskate.  A racking cane costs less than $10 and will make your life infinitely easier.  They also come in smaller lengths for racking out of gallon-size jugs.  These are worth owning too.  Trying to rack out of a gallon jug using a full-size auto-siphon is a challenge and will almost always kick up the sediment at the bottom before you get a good flow going.

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Hydrometer

How do you know how much alcohol you've got?  With a hydrometer.  A hydrometer looks like a glass thermometer with a weight at the bottom.  It measures specific gravity, which is the density of a liquid, relative to water.  A liquid with lots of sugar dissolved in it is denser than water, which makes the hydrometer more buoyant.  As the yeast converts the sugar into alcohol, the liquid becomes less dense and the hydrometer will float at a lower level.  By measuring the specific gravity before and after fermentation, calculating the difference, and comparing that number to one of several hydrometer scales (Balling, Brix, or Plato), one can determine the alcohol by volume (ABV) of a beer or wine.  This tool is very useful for determining when something has fermented to dryness (zero remaining sugar).