For Thermos bottles (the type you drink out of), the bottom of the flask ends in a small diameter glass tubing. Large glass lab dewars often have a large-bore (1", e.g.) glass tube, the better to pump down quickly and deeply. It often comes out of the side near the top, for convenience. The transition to the vacuum system is made by slipping over a special brass or stainless collar that has a compression fitting similar to those used to connect 3/8" copper water tubing into the angle stop valve under your bathroom sink. The compression seal is made by a rubber O-ring instead of a brass ferrule, with a little high-vacuum silicone grease to ensure a good seal. A length of flexible piping, which can be heavy-walled rubber or a stainless steel bellows, provides strain relief between the glass dewar and the valve at the input port to the vacuum pump. In the lab, the dewar is always connected. The Thermos bottle, on the other hand, is pumped down and then its little glass tube is heated with a torch, sealed, and broken free. In some Thermos bottles, you can remove the bottom and see this.
Of course more exotic systems are available to address special requirements.