I used to write incantations and chants when I was bored, but I don't know whether my way is what you're looking for. I used different types of contracts to model for the invocations.
My amateur way
Generally, the tone is slightly aggressive. The words are carefully picked, sophisticated and poetic. Some incantations could be 'Come to me' written in a few different ways and slapped together plus some elements of promise. This does not really follow a contract, it is just a call.
Think about a contract?
1) State the parties involved and make them sound awesome. So, introduce who is the caller and who or what is the summoned.
2) The exchanges. "I will do this if you do this for me" is a good place to start.
Think about a Hittite covenant or promise? (But not exactly because I am omitting and changing up some parts)
1) The preamble: Lists the sovereign's titles. So, list whatever the caller is using titles, attributes and genealogy. King of...Guardian of...Knight of...Mother of...Average person of this nation...Son of...Descendant of...
2) The witnesses: Often times, forces of nature is called upon to witness the promise. "I call upon the coldest gales from Earth's lips, the raging seas of death and everything hiding behind shadows of night or light of day. Come forth and witness my calling to (whatever is being called)!"
3) The blessings and curses: Summons are not exactly promises made from a sovereign to a vassal, but maybe you can list what the summoner would do to keep the summoned interested or happy.
Of Course, there is always the lame way of begging the summoned
I won't get into this too much because it is boring and terrible to read, but it is an option. Just flatter the summoned until they appear.
"Oh, great Dragon of the East, please assist me! Allow me to be graced with your presence and show me thy righteousness by helping me?"
Well, I may be overdoing it and it seems off. If done well, it has the potential to be interesting.
I apologize for writing so much and repeating a few things. I hope it helps and there are some great sources online. Some witchy places also have good phrases if you are fine with exploring witches. Witchcraft for some people is a huge nono, but I learned about it to make chants and summoning phrases.
