Modulating up a half step is probably one of the most common modulations you will use. It is very common especially when accompanying singers. Fortunately, there is a simple little formula that makes it very easy.
Be sure not to start this modulation while any singer or instrument is still in the old key. Once you are able you simply need to do two things:
1. Step down two whole steps in the bass.
2.Change from a I chord in the old key to a V7 chord in the new key.
Remember that the V7 is the important chord that will allow you to resolve to the I chord in the new key. Here is a simple example of this modulation:
Of course, after playing the V7, go to the I chord in the new key. You can definitely spice this modulation up, but for the time being, I will leave that to your own creativity. There are left hand octave runs that work and you can play all kinds of patterns on the V7 chord. Learn the chords first before you try to get fancy.