There are several ways to do what I think you want:
1) Insert the new row, reread all the rows and build the display.
2) Insert the row, redisplay all data that was posted without hitting the database again
3) Send the new data to the server without posting the form (Ajax, etc)
#1 is probably the easiest, because you'll be building the display the same way whether data was just added or not, but #2 isn't that much more complicated. Since you're just learning the technology, I suggest #1. Don't worry about the inefficiency of the extra database read, it's very fast. And you can always move on to #2 or 3 after you're more comfortable writing code.