The beauty of hand piecing is in the handwork and the time you give to create your quilt. It is time consuming but hugely satisfying and with care it will last just as well as a machine pieced quilt.
Like with machine piecing, good preparation is your friend.
Read your pattern all the way through if you are using one and follow it in order.
Cut out your pieces ACCURATELY according to the pattern. Using a rotary cutter and cutting mat is the best and quickest way to achieve this. But you can also mark your fabric with a fabric marker or pencil and cut them out with scissors.
Next you need to mark your stitch line ready for sewing. You can buy 1/4'' wide rulers or just use a normal ruler. You only need to draw your stitch line on one of each pair of pieces you will be sewing together. Mark your fabric on the back and make sure you draw your stitch line EXACTLY 1/4'' in from the edge of your fabric.
Use whatever needle suits you best but a Sharps needle is a good choice here in whatever size is comfortable.
Cotton thread in a 40 or 50 weight is best but if you only have polyester in the house it will be fine.
Place your first two pieces of fabric together, right sides together, edges aligned. Thread your needle and make a quilters knot.
Sew a running stitch all along your stitch line no bigger than 3mm. You can do a back stich every inch or so to help strengthen your seam. When you reach the end of the line tie a good knot or do a few stitches on top of each other to secure.
Repeat as per the pattern instructions.
Take your time and enjoy the process. Hand piecing is nice because you can chat to friends and loved ones while you do it, watch telly, even take a few blocks with you when you go out!