* Check the sticker: Look for a sticker on the driver's side doorjamb or in the owner's manual. This sticker will list the maximum towing capacity for your vehicle's configuration.
* Consult your owner's manual: This is the definitive source for your vehicle's specifications.
Without knowing the specific engine and drivetrain of your 1999 S10 Blazer, any number I provide would be unreliable and potentially dangerous. Always rely on the information provided by the manufacturer.