If the church teaches that the dead cannot pray for the living, how do we believe that saints can intercede for us?

The Catholic Church does not teach that the dead cannot pray for the living. If what you mean by ‘dead’ is about those in hell then you are right about it, they will not be able to pray at all, forget praying for others.

The Church not only consists of people who live on this earth, but it is a communion of people here on earth, those in purgatory, and the saints, angels, and the triune God. Jesus says in John 11:25, “I am the resurrection and the life. The one who believes in me will live, even though they die”. 

This is a question primarily raised by protestants refuting the Catholic understanding of the intercession of saints. One of the scripture our separated brothers quote is Psalms 115: 17. The dead do not praise the LORD, nor do any who go down into silence. but if you read further, the next line says (115: 18) But we will bless the LORD from this time forth and forevermore. Praise the LORD! David clearly says that we will bless the lord for “forever.” David is sure that he will die, but still, said that he would praise the lord ‘forever.’ From this, it is evident that ‘death’ David refers to is spiritual death of a person.

A man who has sinned won’t be able to praise God in his spirit (Sirach 15:9). The prayer of a righteous person is powerful and effective. James 5:16. So the prayers of saints are of more value and effect. That is what the Church teaches. Just like we intercede for others around us, the saints are interceding for all of us especially when we ask. Because of the brotherhood, we share with the righteous in heaven, do not hesitate to ask prayers.