I'm Interested In Learning How To Sew. What Basic Equipment Do I Need To Get Started?

Of course, the first thing you need to buy is a sewing machine. Start with a very basic one (graduating eventually to a serger or a machine that will do embroidery, etc.) that includes a zigzag function for buttonholes. A good machine can cost as little as $100 at a discount store; check the second-hand stores first for real bargains.
Buy two types of good-quality sewing shears: straight-edge and pinking shears. The latter cut with a diamond pattern to finish seams.
Small items you will initially need are:
-- Dressmaker's straight pins
-- A variety of basic thread colours, to be expanded upon as you progress
-- A measuring tape and yardstick
-- A seam ripper
-- Hand-sewing needles for hems
-- Two yards of half-inch elastic for waistbands
-- Tracing paper and a wheel for transferring pattern marks onto the fabric
If you don't already have one, you'll also need an iron and ironing board for "press-as-you-go" clothing construction.
Start with patterns labelled "beginner," "easy," or "two-hour." But for your very first project, consider making something as easy as a pillowcase, without a pattern.
Start with easy-to-handle fabrics like tightly woven cotton. An organza, silk, or taffeta summer dress is beautiful, but the fabric is a pain with which to work, and requires intermediate skills.
Start with solid colours or a small, all-over pattern like flowers so you do not have to worry about matching plaids at the seams.
Ask your fabric store clerks for a lot of advice. Or consider taking a class in sewing offered by the store.