Here is a brief walkthrough of the strategies you can employ while solving a Killer Sudoku puzzle. It assumes you are familiar with the basic rules and strategies of classic Sudoku, all of which apply but are not covered here.
First some basic principles and terminology.
All 81 cells are divided into what are called cages (surrounded by dotted lines). There may be 2 to 5 cells per cage. The number shown in the upper left of each cage is the total of the cells in that cage. In the highlighted cage to the right, the three cells total 19.
Also, no cage may contain duplicate numbers.
The same other rules of Sudoku apply - that is each row, column and block contain the numbers 1 - 9.
You will note that no given cell values are present at the start. This walkthrough will help you get started.
In solving any Killer Sudoku, it is useful to know all the combination of numbers that make up the outstanding total of a cage. DKM Killer Sudoku has a very useful tool in this regard - clicking the combo icon at the top will show a dialog where you can enter the number of unknown cells and their total to see all combinations. If the dialog obscures any cells you may want to examine, you can drag in anywhere by the titlebar.