There are particular sticking patterns which lend themselves to playing on different surfaces to create accents. The most common of these patterns is called the paradiddle. The basic paradiddle pattern is shown here.
Play this pattern many times until you have it memorised. Try the next few examples, which apply the paradiddle to different parts of the kit.
Once you have mastered the previous example, try using it as a fill:
Shakers come in a huge variety of shapes and sizes from small egg shakers to Latin and Central American maracas to the West African shekere. The one thing that they all have in common is that they produce their sound through small beads hitting a surface of the shaker. Most instruments like this require a lot of coordination and practice to get the beads moving in time and are capable of producing many more sounds than at first may be thought.
There are many other ways of using the paradiddle between various parts of the drumkit. The paradiddle is an example of a drum rudiment. Rudiments are specific sticking patterns which vary the combination of left and right hand movements. The paradiddle is only one of 28 basic rudiments. To become a good drummer, it is worth eventually learning all of the rudiments and applying them to the drumkit. For a detailed study of rudiments, see Progressive Drum Method by Craig Lauritsen.