Welcome to homebrewing!
You can brew small batches with regular kitchen equipment, on the stove. Using malt extract is the easiest. For ingredients, visit a Local HomeBrew Store (LHBS) if there's one nearby.
After the boil, chill it by putting the kettle/pot(s) in the sink with cold water. You may need to refresh the chilling water once or twice to get it cool enough, and maybe add some ice toward the end.
When it's down to low room temps (65-70), pour the wort into a suitable fermentation vessel, pitch the yeast and let ferment in a cool place, or look up "swamp cooler." and variations thereof.
Temperature control during fermentation is quite important.