Officially, you use an anti-static wristband grounded via its attached wire to a metal earth, such as a water pipe, or, in some cases, the earth pin of a mains plug. In reality, this grounds one hand, and gives plenty of scope for static to build one heck of a voltage on the other arm via clothing. Back in the day, at about the same time the firm was issuing "image wear", they started being serious about static, and we got a go with a magic box called static meter (voltmeter with a plastic stick poking out). By pulling on a new wool pullover, we consistently got a reading of 12,000 volts, static band or not.
Best practical way of discharging your static is to wear clothing recently laundered, with fabric conditioner in the final rinse, wear the anti static band, and touch the earth connection with your other hand just before handling the component and/or board. And don't touch the metal bits of the memory board. The conditioner leaves the cloth slightly conductive, and gives the static somewhere to go, so the harmful voltage never builds. If you hear a crackling sound when pulling clothing on, you got static.