It is not clear to me what data is to be in the DataGridView. You say that all the data in the TextBoxes are from one table. Does the data in the DataGridView come from and/or go to another table?
There are many ways to use databases in .Net. It takes time to learn each one. I suggest you learn about using the Entity Framework; you can find articles in this web site about that.
A term that is often used to describe the type of form you have is "master/detail". In other words, your table with party name code, date, received by, ref, vehicle type and reg is a table with "master" records and the serial, description, quantity and prices are in another table of detail recirds. You can look for articles about applications like that.