To find it, you'll need to:
1. Locate the underhood fuse block: This is usually a plastic box near the battery, often attached to the inner fender.
2. Consult your owner's manual: The manual should have a diagram showing the location of all the fuses and relays. This is the best way to be sure.
3. Look for a relay that's labeled "A/C," "AC," or something similar: The relay itself may have a label or markings.
4. Check for a relay that's likely to control a high-power device: AC compressors require a significant amount of current, so the relay associated with it will likely be a larger one.
If you can't find it using your owner's manual or by visual inspection, you may need to consult a wiring diagram specific to your 1997 Chevy S10. A local auto parts store may be able to provide one or help you identify the relay.