Hey I am fairly new to hand quilting also. I find that a quilt hoop helps keep the fabric smooth underneath. Start in the center and work out. I also recommend a hoop only large enough that you can comfortable reach your hand up and under to reach to be able to do the stitching. The first hoop I bought about killed me, so I bought a 14" hoop (I think) and find it way easier.
Remember it is suppose to be relaxing and enjoyable.
Diane