They (allegedly) would have taken blankets that had been used by smallpox sufferers and distributed them to the Native Americans at their fort. British soldiers were inoculated against smallpox, so accidental infection wouldn't have been an issue.
Keep in mind, this was a single incident, we don't know if it worked, or if it was even carried out. The only source is Amherst himself suggesting it as a way to wipe out the "savages." There's absolutely no other proof that it actually happened.
Most the time, white settlers were plenty good at spreading smallpox to Native American populations without needing to do it intentionally.