The above diagram may look confusing... fear not, it's one of the most common methods of explaining notes on the guitar, and is actually quite easy to read. The above represents the neck of the guitar, when looked at head on. The first vertical line on the left of the diagram is the sixth string. The line to the right of that is the fifth string. And so on. The horizontal lines in the diagram represent the frets on the guitar... the space between the top horizontal line, and the one below it is the first fret. The space between that second horizontal line from the top and the one below it is the second fret. And so on. The "0" above the diagram represents the open string for the string it is positioned above. Finally, the black dots are indicators that these notes should be played.
Start by using your pick to play the open sixth string. Next, take the first finger on your fretting hand (remembering to curl it), and place it on the first fret of the sixth string. Apply a significant amount of downward pressure to the string, and strike the string with your pick.
Now, take your second finger, place it on the second fret of the guitar (you can take your first finger off), and again strike the sixth string with the pick.
Now, repeat the same process on the third fret, using your third finger. And lastly, on the fourth fret, using your fourth finger. There! You've played all the notes on the sixth string. Now, move to the fifth string... start by playing the open string, then play frets one, two, three and four.
Repeat this process for each string, altering it only on the third string. On this third string, play only up to the third fret. When you've played all the way up to the first string, fourth fret, you've completed the exercise.