There are two kinds of stitches you should know for fursuit repairs.
One is a hidden stitch and one is your standard back n' forth stitch. There both pretty much the same just the reverse.
Standard Seam
If a seam on your body suit or hand paws breaks you will want to know this.
First you will take a thread and needle "should probably use a strong thread" and knot the end of the thread. You will want to start sewing the seam about 1 to 2 inches away from where the stitching broke or ripped. Put the needle through both pieces of fur (bellow rah edge" and back through and knot it so the thread doesn't slip out and it can't go anywhere from that point.
You will then start going back in forth with the thread and needle going down the line where the stitching broke or ripped. Make sure you pull the thread snug with each stitch, don't leave it to loose or to pull it to tight.
Keep stitching till you are 1 to 2 inches on the other end of the broken seam. Knot the end and cut off any extra thread that's hanging. Brush out the seam on the other side if you need to
Hidden Stitch
Its basically the opposite of the back and forth stitch. This stitch is good for feet paws, heads, tails... Items you can't get into the rah edge side.
You take your thread and needle "again you probably should use strong thread" and start at one end of the broken seam, (1 to 2 inches from the broken part). You make a knot so the thread will not move from that point.
You start to go back in forth on the fur side, pushing the needle into the thread and right back out of the fur. Again pulling the thread snug with each stitch, not to loose or to tight.
Keep following the seam down till u get 1 to 2 inches on the other side if the broken seam and then knot the thread. Cut off any extra thread and brush out the seam if needed.