The hardest part is break the ice and you alredy did it. There are many companies hiring immediately. The normal process is call the recruter. He/She will gives you some instruccions and maybe a brief interview to know what you are looking for. They want to know since when you hold your CDL or if you have any moving vilotation. They just need to know the status of your CDL.
Here you have some links to take you to the homepage of some companies It is really easy to apply for this companies and they normally hire with not experience at all.