Severe wear or damage to the drive chain and sprocket teeth can be visually inspected, but you cannot easily determine whether wear on the individual pins and rollers of the drive chain has increased its overall length beyond acceptable limits - this is very commonly referred to as "chain stretch". To determine this, the drive chain must be measured.
Because drive chain and sprocket wear varies tremendously, depending on driving conditions and maintenance, the only way to reliably determine when it is time to replace the 'chain & sprockets' is by visually evaluating their condition and measuring the chain length.
If there are cracks on the chain side plates, or there is binding or stiffness as the wheel/chain is rotated, or if the drive 'stretch' exceeds the limit (2% of the total length for non-sealed chains, 1% for sealed chains), then the drive chain must be replaced.