To find it, you'll likely need to:
1. Consult your owner's manual: This is the best place to start. The manual should have a diagram showing the fuse box and relay locations.
2. Look for a fuse/relay box: The box is usually accessible by removing a small access panel under the dashboard, often near the steering column or under the glove compartment.
3. Identify the flasher relay: The flasher relay is usually a small, square or rectangular component. It might be labeled, or you can compare its size and shape to the diagram in your owner's manual (if available). Sometimes they are labeled "Turn Signal" or have a symbol depicting a flashing light.
If you can't find it using these methods, a search online for "2003 Chevy S10 turn signal flasher location" along with images might be helpful. You could also consult a local auto parts store or mechanic.