If you're left handed then this is definitely the algorithm that you'll excel at, and is probably the first you should learn. (If you're right handed handed maybe start with the Rightie algorithm
The key point initially to this algorithm is to move corner pieces into the correct place, but later on in the solve you'll use it in combination with the Rightie to move edge pieces where you'd like them to be.
The steps for the Leftie (Using the notation described on the previous page is) L' U' L U, this is being demonstrated in the following animation.
Practice the above, after a few turns it will become easier, and you should aim in the future to be able to do the Leftie in about 1 second, but don't worry if it's taking you 4 or 5 seconds at this point.
On a solved cube, if you do the Leftie 6 times and don't make any mistakes the cube will be solved again.
Once you have practiced this move for a while so that it becomes somewhat natural, then move on to the daisy.
Step 1 - The Daisy