As you can see, people have very different ideas about prayer. And that's fine. There really is not right or wrong way (unless we're asking for evil things, of course), and that's very important to remember.
I am Catholic, so my experience is a little different. Catholics have not been encouraged to do much prayer out loud unless it is part of the Mass or a memorized prayer (The Lord's Prayer, for example). Many Christian communities believe spontaneous, personal prayer is the only prayer that matters because it is from the heart. No pressure there!
I had the privilege of working with college students who are both very open minded and eager for new experiences but also often limited by the one and only church they attended with their family. I tried to encourage them to embrace all forms of prayer. For some of them that meant becoming more comfortable with spontaneous prayer. For others it meant embracing the richness or our tradition and the prayers that have been written by others. Nothing wrong with using those, especially if they capture what we are truly trying to say.
If you are interested in memorizing someone else's prayer and repeating that at your small group, you should have no trouble finding lots of prayer books at Barnes and Noble. That might be easier at first.
Laurie G. mentioned a formula for offering a prayer. I learned a different one, but still very helpful:
1. Thanksgiving
2. Petition
3. Praise
4. Conclusion
Heavenly Father, thank you for this beautiful day and for the wonderful discussion that we have shared. As we go back to our busy lives this week, I ask that you help us remember the insights we have gain in our time together. We know that you are with us always. Please help us to be ever mindful of our presence. We ask this through Christ our Lord. Amen.
Hang in there, and don't give up. It's important that you become more comfortable, because then you will be able to relax more and truly feel God's presence in your life and in your prayer.