In any airway emergency, oxygenation is the priority. It might be necessary to re-insert a new tracheostomy tube or other tube into the airway, but often, a patient can be (re)oxygenated by less invasive means. A stable, more oxygenated patient is in a much better position to tolerate airway procedures.
If a tracheostomy tube is removed, it can be difficult to know where and how to apply oxygen, as you have two potential airways to manage. Tracheostomy patients may have an altered upper airway which can make delivery of oxygen via the nose and mouth difficult or impossible.
If a patient is breathing spontaneously, applying oxygen to the stoma can be life saving. If they are not breathing, a small or paediatric face-mask, or supraglottic airway (such as a Laryngeal Mask Airway) can be applied to the stoma. This generates the seal required to deliver ventilation breaths. Gas may escape via the upper airways, and a second responder may need close the mouth and nose to allow effective ventilation.
Of course, if the patient has had a laryngectomy, then the stoma is the only route for delivering oxygen to the lungs.
If these methods fail, then attempt face-mask oxygenation or ventilation via the upper airways. [link to the ventilation via the face page]. More invasive methods of managing the airway may be required, such as re-insertion of a new tracheostomy or small endotracheal tube into the stoma, or intubation of the upper airways. These techniques may be difficult and require specialist equipment and staff.