If you're using dry yeast, no starter needed. Just get another pack. Dry yeast is cheaper than making a starter. If you use liquid, then you might want to make a starter.
The most basic thing you need for a starter is a container that you can sanitize, DME, water, and yeast. That's it. I've heard of people using mason jars, milk jugs, or whatever else they can find. I use an erlenmyer flask because I like being able to drop the flask straight into an ice bath to cool it down.
You add your DME to the water, boil, cool to room temp, and then pitch your yeast. Cover your vessel with sanitized tin foil and then shake occasionally throughout the day to keep everything aerated. That's the basics.
If you want, you can add all sorts of contraptions. As with all things homebrew, you can make it as simple or as complicated as you want. I built a DIY stirplate (there are plans all over the internet for this kind of build) to constantly stir my starter which increases the cell count dramatically from the "shake" method. Still, the basics starter is pretty simple.
The reason you want one is because the liquid yeast vials or packs don't have enough yeast to ferment most beers without stressing the yeast out. Then they can produce off flavors (so I'm told) or, in the case of my second batch, they won't eat all the sugar (Stuck fermentation) they can and you'll get a beer that's sweeter than you want. To figure out how much yeast and starter you should make, go to this link http://yeastcalc.com/
. I use it whenever I brew, because I have to do a couple of steps in my starter because my flask is only 1 liter.
Hope this helps.