One thing I have found with begging, and it seems true almost across the board, is that the submissive tends to get what I think is the wrong idea about the purpose.
The purpose of begging is not to get what you want. In fact the orgasm or whatever it is you beg for is actually the interference in the process. The purpose of begging is to humble yourself for your dominant. If you get yourself hung up on the fact that you really want, for example, that elusive orgasm, then your focus is on yourself.
As such you should first remember you are there not for your own pleasure, but for that of your dominant. "Allow me to cum." Should, by definition be replaced by "Allow me to cum FOR YOU."
Self degradation can be fun, if it is what you are into, using his pet name for you can help also, the exact wording will change with the particular dynamics of your individual relationship. But a for example to run with.
"Please Master, I know I am just your dirty little slave slut. You have me turned on so much it hurts, please allow me the pleasure of serving you with my orgasm, of cumming for you."