FL170,
There is a lot of very good advice being given here.
Captain Nomad has touched on the idea of touching the controls as you practice... you should also consider doing it while you are briefing.
I'm sure you have the idea, but for example when you say "I will select Mixture up" make sure you identify and touch the mixture lever. Same goes for the others.
The way I found best was to learn the outline of the brief (ie the order), and add in the relevant details on the day, especially when you start flying more than one type. This makes you actually think about the relevant items. The order is also a good way to make sure you don't forget anything.
We can all parrot out a brief very quickly, but it should really be like a converstation, thinking about what to say.
My biggest tip - remember you are briefing YOURSELF as much as the other guy.