I only pray along in heart and mind with people I know for a fact I am in full agreement with. Other than that, I listen intently, and ask the Most High to let His will be done, and if they are praying in vain or ignorantly, I ask the Most High to reveal himself to that person so that they may learn how to approach Him and how to gain his listening ear.

This was a real question for me before too, I had to really pray and seek the direction of the Most High. I've been in prayer with people before and had people pray arrogantly, ignorantly, for unholy things that I would never go before the Father for, I've even had people pray and their prayer be in direct conflict of something I have prayed about. How can I honestly pray with someone who is praying against my own prayer? The solution that was given me was to pray from a position of support. I am there to support my brother or sister but if during that prayer I find that the heart, mind or aim of that prayer is not righteous etc... thats when I emply the alternate prayer and ask that the Most High will be done.

Matthew 6(for safety) Read entire chapter for clarity. verse 8 thru 13 and the Spirit of Yahuah will speak to you if there is more you need to say. Romans 8:26
Likewise the Spirit also helpeth our infirmities: for we know not what we should pray for as we ought: but the Spirit itself maketh intercession for us with groanings which cannot be uttered. The process I hold to

this is a good question, depends on what the prayer is. but usually, I listen and stay still while in YAHs presence, allowing His will to be done. sometimes I also do silent prayers, where so much comes in my mind with the exact words but I call those "silent prayers" from the Ruach. Instead of waiting my turn to say them, I started saying so be it after each prayer inside of me. Then if Im not led to pray after the person, I won't because its already done. I started learning this about how Ruach Hakodesh will pray and intercede for you. Also knowing and believing that YAH has heard you. so its not for the glory or esteem of your prayer, but just to be heard from YAH. Those prayers are powerful too. I realized that there will be times I freeze or cant get those exact words out that I heard when its my turn. So my understanding is that Ruach already prayed them. If its on my Ruach to pray, then it will come out exactly as I received it for the situation. Its also good to keep a notebook around too, so you can write it down if led.