Cracks in a clay oven are normal, so there is nothing to worry about and you do not have to fill them every time they appear. But if you do want to fill a crack then it's just a simple case of using some spare clay/sand mix (or make up a small batch if you don't have any left) and fill the crack.
If you then use a sponge float to smooth over the repair, you can make a very neat and tidy job.