shaM is an ancient verbal root meaning the cessation of activity, getting tired from ritual etc., and has cognates in Greek: in derivatives, the prominent meaning is calmness, auspiciousness, etc. but also has tinges of death in some places. The root kR means to do (cognate with the root of English create), so shaMkara is someone who makes auspicious etc. This is an epithet of shiva, the easily pleased, supremely powerful, ascetic artist, final destroyer of all creation amongst the Hindu trinity.
sad is similarly an old root, cognate with and meaning English sit. It has the sense of sitting down (somewhat indecently) or sinking down, being destroyed etc. With the prefix pra, cognate with and having a meaning similar to English fore, the negative senses are removed, and prasad means to fall under someone's influence, to settle down, become clear, become glad, be successful, be calm, be pleased, appease or ask etc. prasAda is the corresponding noun, and often means a gift received out of someone's pleasure, i.e., a gratuity; especially when referring to divine gift. In every day usage, for example, the auspicious food which was offered in prayer to the deity to be consumed later is called prasAda.
shaMkara prasAda would therefore mean a gift from shiva. In most North Indian pronunciation today the final -a (which otherwise is a schwa, somewhat like the a- in English about) is not pronounced. sh- as in English sugar, -s- and -M- as in English sing, A as in English car. word stress is not a marked feature of any of these languages.