I am no expert, but I just finished my first quilt (a baby quilt) and gave it to a friend - it came out pretty well so I'll attempt to help you! If you have finished all of the piecing, then you are ready for the hard part, the quilting and binding. The steps are in this order
1. Make your sandwich - quilt top first, then batting, then backing. Pin it together with the safety pins about two - three inches apart and not in the way of where you will want to be putting your quilting stiches - yes, this will ba a lot of safety pins! I like a 100% cotton batting - some have a scrim that makes it hard to hand quilt, so if that's what you're planning then get one with no scrim. Let the batting be larger than the quilt top - you will cut it to size when you bind.
2. Quilt your sandwich however you want, hand or machine. There are lots of books on this. The easiest is "stitching in the ditch" - i.e., in your piecing seam lines. Machine quilting is challenging any way you do it because of the bulk of the fabric, so try to keep it simple.
3. Bind your quilt. I thought this would be hard but it's easy. Most quilting books will show you how to bind your quilt with perfect mitered corners - the method works well.
Congrats to you for making your own quilt pattern - I'm impressed!
I'm sure OPs will have some good tips or clarifications . .