Leenia, Try it first on the lower string cause that's the easiest:

place a finger of your left hand on any fret on a lower string, then pluck with your right hand. As soon as you pluck the note, then with the left hand finger, keep the string held down but move the string over a little (towards yourself or away from yourself) which will cause the pitch to be altered higher. You can bend the note until it is one half step up, which enables you to play those desired "blues" notes.
Experiment with this until you get more comfortable consistently getting the right pitch. It takes a good ear to get the correct pitch, though.