There are many ways to approach modulation in composition. In pop music the most common kind is direct or abrupt modulation. What this means is that you just move directly to the new key without in any way setting up the change of key with some carefully chosen chords to link the two keys.
The mighty Stevie Wonder is a great fan of direct modulation. If you go to about 3:50 in the video below you will hear the final chorus repeated, each time it goes up a semitone – this is direct modulation to a new key.
The NME has an excellent list of LIFE AFFIRMING KEY CHANGE SONGS here.
Modulation is a central aspect of most classical music where composer’s have used a range of techniques to move fluidly from one key to another. It is also a feature of many jazz standard songs which include extended harmony and modulation.
In both the above examples pivot chords are often used to help link from the original key to a new one.