as far as I know, if you select complete deletion it means that all the gaps in your sequence will be eliminated as you consider them not informative.
In pairwise deletion, the decision is made by comparisons among taxa. Then a character will be excluded when it os abset in one of two taxa compared.
Regarding partial deletion I don't wnat to misinform you as I have not used it and I don't really know if the software I usually use have the option.
Here I post a likn of one software "MEGA" that explains with an example how it treats each gaps depending on what you choose. http://www.megasoftware.net/web_help_7/rh_alignment_gaps_and_sites_with_missing_information.htm
I hope it helps a little bit
Pairwise deletion is the most clear solution while avoiding the lost of too much data,
I advice also to look at indels and the information they can cinvey, if you need it you can code it for futher analysis in PAUP or BEAST, with seqstate.
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