I'm writing this after three and a half hours in a dentist's chair; it will not be exhaustive.
As I've written before, I often use published prayers, particularly older ones and mostly the form known as the collect (accent on the first syllable). But I rarely use them untouched.
Here are three ways to modify a prayer you might find.
First, give in an introduction. If it's not clear why you are using a topical prayer, introduce it and bid the congregation to pray. Second, to make the prayer more fitting to the occasion, insert petitions. Third, if the prayer has phrasing that broadly impedes prayer, modify it, but try to keep the rhythm intact. This one is, I think, abused as license to do what you want, no matter how it flows thereafter. I'll retain some male language for God, but will smooth out excesses; I'll also remove generic male language where men means human beings. More about inclusion in prayer some time when my mouth doesn't throb so much.
Here's a worked example, from the section "Prayers for Family; Parents and Children; Children’s Sunday" in Additional Prayers and Collects from Hymns of the Spirit.
Here is how it originally appears:
Almighty Father of all, who dost set the children of men in families, enable us, we pray thee, so to guide the children committed to our care that they may love the ways of truth and of righteousness, of peace and of goodwill. Fulﬁll in them our divinest dreams, and through them carry forward the coming of thy kingdom upon earth. Amen.
Here is how I might change it.
Let us pray for children in the church :
Our One Parent, universal and gracious, who dost set children in families, enable us, we pray thee, so to guide those children committed to our care, especially Andrea, Bartholomew and Chiana, that they may love the ways of truth and of righteousness, of peace and of goodwill. Fulﬁll in them our divinest dreams, and through them carry forward the coming of thy kingdom upon earth. Amen.
These are all straight-forward, common-sense changes… unless you've never done it. Using prayer resources is more than pulling them out of the book.