The first things students need to know or be reminded of before you introduce the subject of possessive adjectives are (1) how Spanish indicates ownership or possession, using the verb ser + de and (2) what adjectives are and (3) how they have to agree with the nouns they modify. This will be very important, because English-speaking students of Spanish tend to make their possessive adjectives agree in gender and number with the possessor.
Therefore, begin by introducing a few sentences such as these:
El libro es del profesor.
El carro es de nosotros.
La casa es de nosotros.
Los gatos son de ella.
Point out that the use of ser + de is the way that Spanish deals with ownership, and that English uses apostrophe s, so that in English, we say the boy's bicycle instead of the bicyle of the boy. Be sure they see how the words reverse order.
Next, tell them that there is another way in both languages to show possession or ownership: by using possessive adjectives to directly modify the noun. So we could say his bicycle or, looking back at our examples: his book, our car, our house and her cats.
Write the Spanish possessive adjectives on the board, in the six-box paradigm for the three singular and three plural gramamtical persons. Write mi/mis on the upper left, nuestro, nuestra, nuestros, nuestras to the right of that box. Below mi/mis, on the left, write tu/tus, and likewise to its right, the plural possessive adjectives correponding to vosotros usage -- vuestro, vuestra, vuestros, vuestras. Below tu/tus, write su/sus and to its right su/sus again, beneath the vuestro, etc., forms.
The next step is critical. Ask them how to say my bicycle (mi bicicleta), and continue with the most intuitively easy forms, avoiding the nuestro, etc., and vuestro, etc. forms. Be sure to put in a plural or two: her cats is a good one. Point out that she is singular but that she owns more than one cat. Ask them why they think sus gatos is correct. Get them to recognize that mi/mis are adjectives. It can be an aha! moment.
Finally, they are ready to translate the examples about our house and our car -- nuestra casa and nuestro carro. Throw in our [female] friends (nuestros amigas) to show that the adjectives agree with the thing "owned" in terms of gender and number -- because they are adjectives like any other in that regard. The gender and number of the possessor is irrelevant.
Drills should do a quick pass off of simple phrases in English, using familiar nouns for the things possessed.