To start a new game press the "New Game" button, if you want to restart, press the "Restart" button, and to give up and show the solution press the "Show Solution" button. When you complete the grid correctly, you'll know, you don't need to do anything! When you press the "Show Solution" button squares will be coloured differently depending on if your values agreed or disagreed with the solution, red squares are ones which disagree, green are ones that agree. Note that some grids have multiple solutions, so this colouring may not always be right.
If you press the "Solve Mode" button the grid will clear, and you can then click the squares to input the grid you want to solve. When you press "Solve!" the solution to the grid will be displayed, if one exists, otherwise an error message will be displayed.