I don't know how to pickle cayenne and jalapeno peppers. I tried putting them in a mason jar w/ vinegar. They didn't last too long because the top rust. I don't know what 'brine' mean and I don't know what 'water bath' mean.
Peppers do well as a "refrigerated pickle" meaning that they don't need to be cooked at all (or brined in advance, or exposed to a water bath). Just pack the clean jar with your peppers and add anywhere from 50%-100% vinegar (the rest water) brought to a boil. They will be fine as long as you don't expect the pickles to last more than about a month. If your lid reacts to the acid, just put a layer of plastic wrap between the lid and the jar. Of course, pickles made like this do need to be kept refrigerated. Salt, sugar, garlic cloves and whole spices are commonly added. Dissolve any salt and sugar in the vinegar, other additives can just be thrown in the jar with the peppers. You can cut up the peppers any way you like or keep them whole. Here's a typical recipe, but the possibilities are endless: http://www.amateurgourmet.com/2013/08/sweet-and-spicy-pickled-peppers.html
EDIT: I should note that "anywhere from 50%-100% vinegar" assumes a vinegar of at least 5% acidity. To expect your peppers to last a month under refrigeration, aim for at least 3% acidity of the "pickle juice". Salt helps too, try to use non-iodized, some people taste a bitterness in pickles made with iodized salt.