Hand quilting is my absolute favourite part of making a quilt. We all make unique colour and design choices but this is where we really leave our mark. You literally see the hand work.
There is no end to the texture and design you can create. I suggest you start simple and experiment. Like machine quilting I recommend expermenting on some scraps to find a stitch length you like for your project and to find your rhythm.
Betweens needles are traditional quilters needles, very thin and sharp for piercing the different layers. Shorter needles will help you get a shorter stitch but you may like the look of a longer stitch and choose a longer needle. Thicker threads require a needle with a large eye and Crewel or Sashiko needles are also popular options. Have a look at this hand quilting starter kit.
You may have a design planned that you want to mark on your fabric or you may want to go free hand following where the design takes you.
Start by knotting your thread securely and burying it under your top later of fabric. Insert you needle and come out where you wish to start quilting. Pull your thread through and give it a tug until the knot 'pops' under the fabric.
Insert your needle, perpendicular, a little way through all layers of fabric, then rock your needle back so you can pierce it back up through the layers. Pull your needle and thread all the way through and repeat. If you are using a longer needle you might be able to load more than one stitch on it at a time.
When you reach the end of your line or near the end of your thread, knot your fabric and bury again.
Some quilters also like to use a hoop to help prevent fabric slippage and get more even stitches. I have some 14'' ones here if you want to take a look. Sometimes I use one, sometimes I don't.