To start go with the buckets, etc demonstrated in the link.
If you have a decent stock-pot that holds a couple gallons you can do an extract partial boil on the stove in the kitchen and brew some pretty decent beer very easily.
But, if you get into this thing serious then there is equipment to buy- and I would start with a decent sized brew kettle. Secondly, give some thought to the temperature you'll be fermenting in. For ales you want to have a range between 60 and 70 Fahrenheit. Often this takes special measures in both summer and winter.
Thirdly, it's never too soon to discuss water. You can't have good beer without water that tastes good. So if your tap water is crap then buy gallon jugs at the store. With extract brewing purified or distilled water works very well.