Adjusting Quartz Watch

It'll need servicing, you can't make a mechanical adjustment to speed up or slow the rate. Quartz crystals vibrate at a specific frequency, 32,768/second if memory serves me right.

 

The first thing is put in a new battery and check rate with a fresh battery. Rate is sensitive to low voltage. If it's still slow, then cleaning is the most useful next step. In a few cases, if your watch has had a hard shock, that can cause the crystal to change frequency, which is pretty much permanent.

Most quartz watches don't have a rate adjustment, though a few do. The quartz crystal is fixed frequency, but a trimmer capacitor was sometimes used in the oscillator circuit in early quartz watches to "pull" the frequency slightly. If the watch has something like this, the range of adjustment will be very small. Another thing is that quartz watches are most accurate when worn, which keeps the case at a constant temperature due to contact with your skin, which keeps the crystal oscillating at a constant frequency. Crystals do change their frequency with temperature, so you might see a 10ppm variance when in uncontrolled temperature environment, versus a 0.5ppm variance if worn on the wrist so your body heat maintains case temperature at a constant level.

There are techniques that could allow a more adjustable quartz movement design, such as a programmable divider, but I'm not aware of any in use in even high-end quartz watches which typically use similar quartz movements as the lower end. What you're paying for isn't the movement but the rest of the watch.