Learning the correct pencil grip can be quite challenging for young children. Activities like cutting with a scissors and using clothes pegs can be very helpful as they help strengthen small muscles in the hand. Using a small binder clip (like the one shown in the picture) on a pencil can help children hugely with pencil grip.
The following website article has some great tips on how to correct pencil grip that you may find helpful:
Furthermore, the next website article has some excellent fine motor activities that can help strengthen hand muscles for all children thus improving writing skills. Some of the activities are very enjoyable for children too so if you are ever stuck for rainy day activities these could come in handy!