The correct form of the phrase in Klingon would be yIn nI' DaSIQjaj 'ej bIchepjaj.
And it breaks down (word for word) like this: "Life long you-it-endure-may and you-be-prosperous-may." Or, in proper English, "May you endure a long life and may you prosper."
Klingon sentence structure is about as complex as it gets. Most people are familiar with the idea that verb endings can indicate person and number. In Spanish, the -o suffix on a verb like hablar (to speak) indicates a first-person singular subject (hablo—I speak) while the -amos suffix indicates a first-person plural subject (hablamos—we speak). But Klingon uses prefixes rather than suffixes for such purposes, and instead of having six or seven of them, like most romance languages, it has 29. There are so many because they indicate not only the person and number of the subject (who is doing) but also of the object (whom it is being done to). In the "Live long and prosper" translation above, for example, the Da- on SIQ indicates a second-person subject and a third-person object ("You endure it"), and the bI- on the verb chep indicates a second-person subject and no object ("You prosper").
Klingon also has a large set of suffixes. Attached to the end of the verbs SIQ and chep is the ending -jaj, which expresses "a desire or wish on the part of the speaker that something take place in the future." Klingon has 36 verb suffixes and 26 noun suffixes that express everything from negation to causality to possession to how willing a speaker is to vouch for the accuracy of what he says. By piling on these suffixes, one after the other, you can pack a lot of meaning on to a single word in Klingon—words like nuHegh'eghrupqa'moHlaHbe'law'lI'neS, which translates roughly to: They are apparently unable to cause us to prepare to resume honorable suicide (in progress).
Just saying a word like this one requires Klingon-like discipline and fortitude. To the layman, the time commitment involved in studying this invented language may seem ridiculous—why not take up a language with practical value, one that might earn you a little respect, or at least not encourage jeers? But Klingon isn't about practicality, or status, or even about love for the original Star Trek series. It's about language for language's sake, and the joy of doing something that's not easy, without regard for worldly recognition. Hence the Klingon Hamlet, which took years to compose and which maybe 100 people can appreciate. What a piece of work is man indeed. Or as Wil'yam Shex'pir put it, toH, chovnatlh Doj ghaH tlhIngan'e'.