Most water bottle holders are made from durable rubber and works by stretching around the neck of plastic water bottles. It is strong enough to hold one liter bottles.
The rubber o-ring is either sewn (nylon material) or crimped (cotton material) to the lanyard material. For cord lanyards the o-ring is first attached to one side of a short segment of webbing with the cord attaching to the other end.
Some water bottle holder lanyards are made longer so it can worn across the chest with the water bottle hanging to one side.