If you're right handed then this is definitely the algorithm that you'll excel at, and is probably the first you should learn. (If you're left handed maybe start with the Leftie algorithm but come back here after to learn 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 Leftie to move edge pieces where you'd like them to be.
The steps for the Rightie (Using the notation described on the previous page is) R U R' 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 Rightie 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 Rightie 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 leftie.
Learn the Leftie algorithm