Something of a new Christian here, five years in. I heard a similar prayer guide to what Paul K mentioned, but instead of the acronym ACTS, it's PRAY...Praise, Repent, Ask, Yield:

P(raise) God for his attributes, actions, love for us, salvation, etc.
R(epent) of your sins anew, asking forgiveness for them.
A(sk) for your prayer request, of course in humility, supplication
Y(ield) your desires to God's plans which are greater than ours and better for us.

If I'm not mistaken, The Lord's Prayer follows this very same format, so this structure of prayer is God-given, directly. Pretty solid foundation for a prayer structure, no?