The first step to understanding the differences between these three linguistic tools, is to define them.
Translation by definition means: the process of translating words or text from one language into another. Translation is useful for a number of things, and is used quite frequently. There are translational tools such as Google Translate that can help you understand meaning from one language to the next. However, translation is refined skill, and to translate anything of importance requires a fair amount of knowledge on both the language you are translating to, and the topic of which you are translating. Translation errors can be easy to overlook, and the negative consequences can be extreme.
Transcription by definition means: to make a written copy, especially a typewritten copy, of (dictated material, notes taken during a lecture, or other spoken material). Also, from a linguistics perspective it means "to write out in another language or alphabet".
Transcription is the process of listening to something and writing down, as stated in the definition. For Indigenous languages, the most important part of transcription may be the phonetic representation of a language from it's original alphabet, to one of the phonetic alphabets. By transcribing language audio into a more universal form, it allows for clearer analysis of the language for anyone using it in the future. There are two phonetic alphabets worth mentioning for the work that we are doing here in North America.
The international Phonetic Alphabet is a wonderful tool for linguists and language learners world wide. By having a universal set of symbols to represent individual and unique sounds, it allows for the closest phonological representation of sound to be recorded. While there are issues with the IPA, it is still an excellent resource to have.
The north american phonetic alphabet is incredibly useful when working with Indigenous languages here in North America. Many of the Indigenous languages in the region use the North American Phonetic Alphabet for their orthographies over the International Phonetic Alphabet. The North American Phonetic Alphabet is much more refined system, that represents the sounds most commonly found in the languages of North America. However, it is also used elsewhere in the world outside of this continent.
Transliteration by definition means: "to change (letters, words, etc.) into corresponding characters of another alphabet or language". Transliteration is complicated and can easily be confused for transcription and in some cases translation. There are a few practical instances for needing to use transliteration, but the most common is to transfer phonetic information from one alphabet to another, while still retaining the integrity of the phonetic makeup for whatever it is you are transliterating.
An example of a time when you would need to transliterate, is when a language has multiple dialects and orthographies. The language Nłeʔkepmxcin has two orthographies. One is the Americanist orthography, and the other is the Bouchard orthography.
http://mentalfloss.com/article/48795/9-little-translation-mistakes-caused-big-problems http://www.dictionary.com/browse/transcribe http://www.nativlang.com/linguistics/ipa-pronunciation-lessons.php http://www.firstvoices.com/en/nlekepmxcin http://www.internationalphoneticalphabet.org/ipa-sounds/ipa-chart-with-sounds/ http://www.languagegeek.com/salishan/nlekepmxcin.html http://www.dictionary.com/browse/transliterate https://en.wikipedia.org/wiki/International_Phonetic_Alphabet http://www.ablongman.com/html/productinfo/bauman3e/020554925X_ch03.pdf