I'm not a microbiologist, but I am an semi-experienced brewer, and a thinker as well, so take this for what it is worth, it WILL improve your beer and the repeatability of quality beer.

My goal, as stated on the front page of this site, is not to rewrite or duplicate the good, accurate efforts of other people, especially those who have more experience and factual basis for their information than I might. That said, Jamil Zainasheff has provided a great deal of information at his site www.MrMalty.com

I'd suggest checking out the site and doing some reading. If more people would do this we would have a lot less of the typical internet postings about slow starts, strange flavors, stalled fermentations, and my favorite "should I make a starter?"

Another great source of yeast information is from The Maltose Falcons.

Yes, you should make a starter unless you've done the calculations that say the yeast tube or packet that you purchased already has the required number of cells available.

http://www.mrmalty.com/starter_faq.htm

If you have a question about how big the starter needs to be, or how to account for some other variables such as specific gravity, age of the yeast, type of yeast, etc, please see

The Mr Malty Pitching Rate Calculator

How I do it

So now that I've provided info from the most reliable sources that I know... here is what I do each time. You don't need much other than a standard cooking pot, a thermometer, and a container to ferment the starter in. Don't make this tougher than it is!

1. Based on the recipe, check the Mr Malty Pitching Rate Calculator.

2. Buy the suggested amount of yeast packs, or make a starter with the proper number of packs. (yes, it might be required that you use more than one yeast pack for your starter)

3. Boil 1/2 cup Dry Malt Extract (DME) (Also called spraymalt extract) with 2 cups water. Treat the water as if you were going to use it in your beer. This means remove the chlorine, or chloramines that might be present, or buy some bottled "spring water" or drinking water" to use.

Add the malt extract to the water, and it seems that warm water helps it dissolve, but makes it sticky in the package you pur from due to the steam, so never pur directly from a package unless you are using the whole package which is rare. Store the leftover extract in a mason jar or closed container for another time.

For the boil, any pot will work, but I prefer to use a combination of pot and erlenmeyer flask. I like to warm the water in the pot and mix in the extract with a wire whisk, then pour into the flask for the boil. Mixing in a pot is easier and allows me to break up any clumps. You can mix everything cold in the flask as well, and then heat, but if you get clumping, and maybe some extract sticking to the sides of the flask, it can be a PITA.

I also find that mixing first in the pot works well when I make larger starters. I  use only part of the water in the pot, and part in the flask, adding the extract to the pot and mixing, then adding the mix to the water already in the flask. Once you play around you'll find a way that works for you.

Boiling for 15 minutes will sanitize the wort and the flask at the same time, and this reduces the chance of contamination. I add ONE drop of foam control (Fermcap-S) to my starter to reduce the chance of boilovers, and reduce the chance of foam-overs during fermentation. And trust me, one drop of foam control will not stop a boilover if you are not watching your stove set on high!

4. Chill the flask or pot in an ice bath using another pot filled with water and ice. Cover the pot while cooling to prevent contamination. I use a foam stopper in the flask that allows some steam to escape. If you are using a pot, just make sure you have a lid. Sanitize the lid of course. Chill to 70F, measure with a sanitized thermometer. I prefer a digital thermocouple model so I only have a thin probe wire that goes through the foam stopper. Any thermometer will work however.

5. If you are using a flask, aerate the wort by shaking, pumping sanitary air, or adding pure oxygen. With a starter it is easy enough to just shake for a while.

Once the wort is aerated, just sanitize the yeast pack, and your hands, and pitch the yeast into the flask. Place some tin foil, a foam stopper, or an airlock on the flask.

6. If you are using a pot, sanitize a funnel, and the vessel you will use to ferment the starter. You can use ANY kind of container to make your starter, and all you need to be able to do is sanitize it, and be able cover the opening to keep the nasties and bugs out. Glass jugs or big jars work great. Don't stress this part as anything will work fine.

I make sure to wipe the outside of the pot with some sanitizer in case some wort runs down the side of the pot and drips into the fermenting vessel. Pour the wort into the fermenting vessel. As above, properly aerate the wort before pitching the yeast. Sanitize the yeast pack and your hands before pitching.

7. Place in a location with temps around 70F, a bit colder or warmer is no big deal for most yeast strains. You are making a starter and propogating yeast, not making your beer just yet, so don't stress the temps unless they are outside the range for the yeast. Stirplates are best to get the maximum propogation, but shaking the starter now and then really helps, so don't think you have to buy anything special to make a great starter.

8. Let the starter ferment as long as possible. The night before the brew day, place the starter in the fridge to chill it and let theyeast drop to the bottom. When you are ready to pitch the starter into your wort on brewday, pour off the excess liquid, and only pitch the yeast solids into your fermenter. There is no reason to pitch the liquid portions of the starter.

STIRPLATES

The biggest cell counts will be achieved by using a magnetic stirrer or "stirplate." You can find used ones on Ebay that are commercial lab-grade for about $50 all the time. You can build one, but I don't see the point to building one when the commercial ones are made specifically to do what we need, and are built for long run times with exacting magnetic balance. I'm in this hobby to brew beer, not to tinker with cigar boxes and Radio Shack parts :-)

FLASKS

I use 2L and a 5L borosilicate glass (Pyrex) erlenmeyer flasks, and foam stoppers. You don't have to use these, but they can go from the stove, to the ice bath, and on to the stirplate with no issues. WARNING... If you use any type of glass flask on an ELECTRIC COIL STOVE, use a $3 heat diffuser, or you might have the flask shatter due to the uneven heating of the electric coils. I have had this happen before this warning was given by the manufacturers and distributors, so it is not a myth!