To crochet the star you need a crochet hook in needle size 3.0. In rounds you crochet with the puff stitch.
How to crochet a puff stitch
Place the thread over the needle to form a loop and pierce the needle through the thread ring. Place the thread over the needle again and pull it through the ring. This will be repeated until 7 loops are on the needle. Then another thread is put over the needle and pulled through all the loops.
For the first crochet round crochet a thread ring and crochet alternately 5 puff stitches and 2 air stitches
In the 2nd round crochet 3 air stitches, 3 sticks, leave the stitches on the needle and cast off all 3 stitches together. This is repeated 5 times, so that 10 stitch packages are created
The packages are closed with a round warp stitch.
Now the crocheting of the star prongs begins: For this 2 air stitches are crocheted, then from the next stitch sheet 1 firm stitch, 1 wale, 1 double wale, 3 air stitches, 1 double wale, 1 wale, 1 firm stitch, 2 air stitches, 1 warp stitch into the next air stitch sheet. This is repeated until 5 star points are created, with one warp stitch the crochet work is closed.