Inspiratory:Expiratory ratio refers to the ratio of inspiratory time:expiratory time. In normal spontaneous breathing, the expiratory time is about twice as long as the inspiratory time. This gives an I:E ratio of 1:2 and is read "one to two".
This ratio is typically changed in asthmatics due to the prolonged time of expiration. They might have an I:E ratio of 1:3 or 1:4. Even longer expiratory times are required sometimes, but this is best done by an experienced clinician.
An inverse ratio refers to when the I:E ratio is 2:1 or higher and is typically used to ventilate non-compliant lungs. This requires some level of expertise. Consult a senior clinician if you are unsure. Pressure control modes of ventilation should be used when employing inverse ratios as the use of volume control modes might lead to "breath stacking" and an increase in airway pressures.