I'll demonstrate how NOT to do typology by using examples of Catholic apologists twisting the Bible out of shape to squeeze the dogmas about Mary into the scripture.
The types of Mary are supposedly the New Eve, the Ark of the New Covenant and the Queen Mother. But when we examine them we see that they not only aren't types, they don't give the dogmas that Catholic apologists pretend they do.
From the "New Eve" they want to say that Mary was immaculately conceived (that she was born without sin and never sinned through her life). From the "Ark of the New Covenant" they want to say she was perpetually a virgin (even after Jesus' birth) and that she was taken bodily up into heaven at the end of her life. From the "Queen Mother" they want to say she is exalted to the right hand of Jesus and can intercede for us today.
Here are the links to the Catholic sources I mentioned in this teaching.