When looking at the 1 DNA stand (double-helix), how do we know if parent or complement strand is 3-5 or 5-3 end?

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I'm not sure exactly what you mean about "parent" vs "complement" strand when talking about a normal DNA molecule, each strand of the double helix is the complement of the other.  Each strand, look for the phosphate end, that's its 5' end, so the other end of that particular strand is 3'If you're talking about during DNA replication, the growing strand is being built 5' -> 3', so look for the elongating end, that's the 3' end.  The strand that's being used as the guide or template (sometimes called "parental" strand) would have the opposite orientation.  This means if the growing/being built strand is orientated (left to right) 5'->3' then in the drawing, the template strand (left to right) would be orientated 3'- 5'.  I hope that makes sense.  Take a look at the link I'm posting, you'll see a DNA molecule w/two new strands being built on it, each oriented in opposite directions.