1. The underlying form is basically the form that the speaker associates it with. So, for example, in English, we have several different ways of forming the plural. So, we have different plural endings for /kæts/, /dɒɡz/ and /hɔrsɨz// (cats, dogs, and horses) based on the phonetic environment that they occur in. But we still perceive the underlying form to be /s/, as reflected in our writing system. The underlying forms, in this case, /s/, is expressed as the surface forms, or variants, when they are surrounded by phonemes which directly affect how they are expressed. So, in the example above, /s/ remains /s/ when it is preceded by a devoiced consonant. If it is voiced, however, then it also gains the characteristic of voicing and is expressed in its surface formas /z/. The underlying form remains /s/. However, if the word ends in a sibilant- /s/, /z/, /ʃ/, /ʒ/, /tʃ/ or /dʒ/-, then the plural is expressed as /ɨz/ in its surface form. Yet we still perceive the underlying form to be /s/. The phonological environment surrounding the sound is of the greatest importance in determining whether the underlying form is the one expressed or the surface form is instead. There are a few different ways an underlying form can change to a surface form.
As shown, the different changes affect the surface form in different ways. Deletion turns the surface form into no phoneme at all. Insertion inserts a phoneme where none had previously been. Fissure adds two phonemes where there had been only one (the /hɔrsɨz/ case demonstrates this). Fusion causes two separate phonemes to become a single one, perhaps adopting some properties of both; change of value, quite common and demonstrated above by /s/ becoming voiced as /z/ in our cats and dogs example, changes the phoneme into another one entirely; and perhaps less common, change of order simply involves two phonemes switching places. These are all, of course, determined by the phonetic environment surrounding them.
2. In cases of complementary distribution, phonologists seek to find a rule that explains why there is a variant. If a rule is found, then the variant which is subject to the rule is clearly the one subject to the rule, as it can only be explained by it. In complementary distribution, the two sounds are, by necessity, mutually exclusive and cannot occur in the same environment. The underlying form is the form that is not affected directly by a rule. So, for example, in German, which has final devoicing, the end forms of /p/, /t/, and /k/ for /b/, /d/, and /g/ are the variants, since they are subject to the rule in these particular situations, but are only expressed in the way that they are because they happen to be at the end of a syllable, and would be expressed in their normal forms in other environments.
Resources:
Linguistics TA Manual. Stanford University. Retrieved from
http://linguistics.stanford.edu/resources/ta-manual/complementary-distribution.html on 2/19/2013.
Justice, Paul W. (2004) Relevant Linguistics, An introduction to the Structure and Use of
English for Teachers, 2nd Edition, Revised and Expanded. Stanford, California: CSLI Publications.
Crystal, David (1997). The Cambridge Encyclopedia of Language, Second Edition.
Cambridge, New York, Melbourne: Cambridge University Press.
Campbell, Lyle (1999). Historical Linguistics: An Introduction. Cambridge,
Massachusetts: MIT Press.
Hayes, Bruce (2007). “About Phonemes: An Extract from Introductory Phonology by Bruce
Hayes”. Department of Linguistics, UCLA. Retrieved from
http://www.linguistics.ucla.edu/people/hayes/103/HayesOnPhonemes.pdf on 2/19/2013.
Zwicky, A.M (1975). “Settling on an Underlying Form: The English Inflectional Endings”.
Retrieved from http://www.stanford.edu/~zwicky/english-inflectional-endings.pdf on
2/19/2013.