Start Heating Your Water - Measure out 2-3 gallons of water (I start with hot water from the tap since my hot water heater has already done part of the work for me), add that to your pot, cover, and heat the water to around 155-160 degrees.  Ideally you want to use a stainless steel pot with a 4-5 gallon capacity.  You can use aluminum if you need to, but stainless steel is the best route to go.  DO NOT use a non-stick pan from the kitchen cabinet!!!  Those can hold on to flavors that are not desirable in beer.  A dedicated stainless steel pot is best.

Crush your grains - When I first started brewing, I picked up a cheap "Corona-style" grain mill that's typically used for milling corn so I could crush my grains at home.  This keeps the grain fresher for longer periods of time.  The Corona mill worked OK for starting out without investing too much, but if you think you're going to stick with the hobby and move on to All-Grain at some point, I would suggest getting one of the other mills listed below.  I've worked my way up to the MM2 Monster Mill over the years, and that thing is a tank!  And of course you don't need to go out and buy a mill right away if you don't want to. Mostly all online stores and local homebrew shops will mill your grain for you either for free or for a very small fee.  If you happen to order a kit where the grain isn't crushed and you don't have a mill, you can try putting the grain into a heavy-duty plastic baggie and crushing it with a rolling pin.

Steep Your Grains - After you have crushed your grains, put them in a grain bag and add them to your pot.  Steep the grains in 155 degree water for about 30 minutes.  Make sure to agitate the grains a few times during the steep in order to extract the flavor and color.  After 30 minutes, remove the grains after allowing almost all of the liquid to drain from your bag.  You can also use some of the liquid in the pot to gently pour liquid over the bag to help rinse the sugar from the grains.  This is called "sparging" in an all-grain system.  A colander can help hold the grain bag while you sparge with some additional water as well.  Here are a few different types of bags below, including a large bag for people wanting to potentially transition from extract to Brew-In-A-Bag (BIAB) all-grain brewing.  NOTE:  The BIAB option does require a larger kettle, so you'll need something around 7-8 gallons instead of a 4-5 gallon kettle typically used for extract.

Add Malt Extract and Bring to a Boil - You have a couple of options at this point - You can add all your extract at the beginning of the boil, or you can add about 1/3 and add the rest with 15 minutes left in the boil.  The second option is known as "late-extract addition."  I would recommend you go with the "late extract addition" as you will achieve higher hop utilization, lighter color, and cleaner/lighter flavor (in my opinion).  Your brewing liquid is now referred to as wort, which is the combination of water and grain sugars.  **Make sure you watch for boilovers as your wort comes to a boil.  Sticky & burnt-on wort is not fun to clean off a stove if you are brewing inside.  A good quality stainless steel spoon helps with stirring, and you're also able to clean and sanitize it for other uses in your brewery.

Add the Hops - When your wort reaches a boil, you will add whatever bittering hops you have.  These hops will be boiled for 60 minutes.  You may also have flavor and aroma hops.  Flavor hops are usually boiled for 15-30 minutes, and aroma hops are usually boiled from 1-5 minutes.  Some people like to bag their hops in order to have less "gunk" going into the fermenter.  I never found that to be an issue, so I choose to just add them directly to the pot.  If you're interested in either bagging your hops, or pouring your wort through a filter when you transfer from your kettle to your fermenter, here are a couple options:

Cool Your Wort - There are several methods to cool down your wort.  I started out with the Cold Water Bath, then moved on to adding ice directly to my wort along with water, and finally I purchased a wort chiller when I moved up to full boils.

• Cold Water Bath - This is the easiest and cheapest way to cool down your wort after brewing.  You put your beer kettle into the sink, add cold water as high up as you can, and stir the wort until it chills down.  Note:  You will likely need to drain the water and refill with cold water a couple times or start adding ice cubes at the end in order to get the temperature down if your ground water is warmer (think summer brewing).

• Add Ice & Water Directly to Wort - After a few sessions, I came up with this method as a way to speed up the chilling process.  Once my boil had finished, I would put the kettle into a cold water bath and then run to the gas station and grab an 8 lb bag of ice.  I would then add the ice to a sanitized fermenter, pour in my hot wort, and top up with cold water from the tap.  NOTE:  Make sure you trust the source you're getting your ice from!  Their ice production methods are most likely completely sanitary, but I never experienced any issues.  Use this technique at your own risk.

• Use a Wort Chiller - If you are a partial-boil brewer, you can use ice and cold water to make 5.5 gallons and cool off the wort at the same time in your primary fermenter.  If you are a full-boil brewer, you will need to invest in a wort chiller to cool down your beer.  **For ales, you will want your wort to be cooled to 70 degrees.

Transfer Your Beer to a Fermenter - If you haven't already done so, rack or pour your beer into the primary fermenter.  I like to use plastic buckets for my primary fermentation and Better Bottles (or other PET fermenter) for secondary.  Some people say that plastic buckets cause the beer to absorb oxygen whereas glass does not.  After 10+ years of brewing and leaving beer in the plastic bucket for up to 2 months, I can tell you I have never personally experienced any issues.  For longer aging I do like to use the PET fermenters as they have the same properties as glass and do help to reduce any potential oxygen uptake.

Take a Specific Gravity Reading - In order to know how efficient your brewing process is and what your ending % alcohol will be, you need to measure the amount of sugar present in your wort.  This can be done using either a hydrometer or a refractometer.  A hydrometer is typically included with a homebrew equipment starter kit, so you will likely already have one if you purchased one of those.  If not, I've included a link to one below.  A refractometer is nice to have for all-grain brewing as well as extract brewing.  It allows you to take a gravity reading using only a few drops of wort and also without you having to cool down the sample.  However, a refractometer does have issues taking the gravity of samples that contain alcohol.  You need to use a calculator to determine the results.  I like to use a refractometer to take gravity samples before fermentation, and a hydrometer to take samples when I'm ready to bottle or keg.

Pitch Your Yeast - If your are using a liquid yeast smack-pack, you will need to activate that before you start brewing.  If you are using dry yeast, you can just sprinkle the yeast over your cooled wort.  Liquid yeast is nice for brewing specific beer styles, since there are many more regional yeast varieties available in liquid form.  You can also follow my process of Saving & Reusing Yeast, which will cut down on the added cost of liquid yeast strains.  Dry yeast is slowly adding more and more strains though, and they have a much longer shelf life as well as a higher cell count per packet.  I tend to use more dry yeast (Fermentis US-05) these days since I brew a lot of American styles, but try out various types and see which you prefer for your different brews.

Let the Beer Ferment - Store your fermenter in a cool and dark place.  Basements work very well, but make sure it doesn't get too cold in the winter.  An average strength beer usually takes 3-7 days to fully ferment, so be patient.  I like to keep my beer in the primary fermenter for at least two weeks to make sure fermentation has fully completed.  You may also choose to rack your beer to a secondary fermenter where it will clear and age, but I have not found this necessary with most beers.

Bottle Your Beer -  If you're in a hurry to get your beer bottled, you can start taking hydrometer readings a couple days after your airlock activity looks like it has stopped.  You want to be sure to get three hydrometer samples that are the same over the course of three days in order to ensure that your fermentation is complete.  If you don't want to mess with this step, just give your beer two weeks in the primary and it should be done by then.  ***If your beer has not stopped fermenting, you will likely have exploding bottles which are very dangerous.  To bottle, you will need to dissolve your priming sugar in 1 cup of water and boil in the microwave for 15 minutes.  While your boiling the sugar mixture, sanitize 55 12oz bottles or 26 22oz bottles and allow them to drain.  Also sanitize enough caps to fit all the bottles.  Add the cooled sugar mixture to your sanitized bottling bucket, and rack your beer on top of it.  This sugar mixture will be what creates carbonation in your bottled beer.  Attach your tubing and bottling wand to the spigot of the bottling bucket.  Fill each bottle to the top and then put on the cap.  After your are done filling bottles, use your bottle-capper to secure the caps to the bottles.

Age Your Beer - Make sure to store your beer in a cool and dry place, but don't let the temperature get too low.  The remaining yeast will eat the sugar in order to create carbonation, and they can't function if the temperature is too low.  Many people use the general 1-2-3 guideline for beer making.  One week for primary fermentation, two weeks for secondary fermentation, and three weeks in the bottle or keg.  For normal gravity beers, this guideline usually works well.  Since I usually skip secondary fermentation, I just give my beer and extra week or two in primary and a little longer in the bottle/keg. 

Enjoy! - I usually try one of my bottled beers a week or so after I bottle to see how the carbonation process is coming along.  This will tell me how the beer is progressing as well as if the yeast is at the right temperature to create carbonation.  Usually, the longer you can wait to drink your beer, the better it will be.  Good luck & happy brewing!