Assuming you mean the typical fragmentation grenade (they don't make huge explosions like in the movies), modern grenades work like this:
You remove a pin (NOT with your teeth!), which allows a spring-loaded "spoon" to be released, thus arming the grenade. However, the spoon is normally held in place with the hand until the grenade is deployed (ie, the spoon springs off when you throw the grenade), arming the device. Up to this point you can put the pin back in, retaining the spoon and rendering the device safe (in theory - accidents happen).
Once the spoon ejects, after a delay of a few seconds (depends on the fuse), a bursting charge scatters fragments of casing andf notches with over a few meters range (more for defenive type grenades, less for offensive ones intended to be thrown while advancing)
That's basically it. High-tech grenades may have electrenic fuses (though mechanical probably remains popular for confiodence reasons).