That's extremely easy to replace. You go to a local parts store and get a "Stabilizer bar end link". It comes in a few parts. 4 Bushings, 4 washers, a sleeve, a long bolt, and a nut (Probably with plastic threads on the inside.
You take this one off, take everything off the new one except for 1 washer/bushing. Put the bolt halfway in the control arm hole (The bottom hole, where it's still attatched in the pic) add another bushing, followed by another washer, then the sleeve, then another washer, and another bushing. Push the bolt through the stabilizer bar, put the last bushing/washer on, followed by the nut. Then tighten. It's that easy. Should'nt take more than 15 minutes, 45 minutes if it's covered in rust. Yours looks to be clean, but you're new to this. So, I'd suggest about 30 minutes for you to do them. They really are very simple, and when you do them, You'll remember how to do them forever...seriously.
1999 Chevrolet Camaro SS (PC'd)
1994 Chevrolet Beretta Z26 Q4 (W41 M90'd)
2004 Chevrolet Silverado 2500 (4WD)
My wife's cars:
1971 Dodge Charger SE (stock and original 383 auto)
2004 Subaru Impreza WRX (kid-hauler)