There are several threads on neuronal culture troubleshooting here on ResearchGate. Many of the techniques that work for rats also work for mice. You will need to decide which part of the brain and which age to work with. In my experience, embryonic cortex (approx. E 17) is the easiest tissue with which to get lots of viable material.
As I am sure you will see on the thread provided in Jill's comment, there are several ways to produce primary neuronal cultures. I have attached the protocols used in my lab at MIT. I have worked extensively with these protocols and find that they are ideal for people attempting this procedure for the first time. In my opinion, the key to a successful culture is the age of the tissue, the efficiency of tissue dissociation, and the cleanliness of the plated cells (i.e. lack of cellular debris). Primary culture is not easy (it took me 3 months to get a surviving culture, 6-10 months to "perfect" the system), so don't be too discouraged if you fail the first few times. Please let me know if you have any specific questions about the protocol.