Taking into consideration that NOT everyone watches that particular movie or series you are referring to, the following is recommended:

suggestion: take screen shots of the credits part containing info on the song title/singer/lyricist/composer

example:

(thanks Vicky for providing this particular screen shot)

notice that the chinese characters coming after the <> or () of the song title roughly means "sung by"

for ATV/SINGAPORE series:  the song title/singer/lyricist/composer will usually be displayed in the ENDING credits

for TAIWANESE/CHINESE MAINLAND series:  the song title/singer/lyricist/composer can either be displayed in the OPENING or ENDING credits or BOTH (opening for opening theme, ending for ending theme, or ending for all songs)

for TVB series:  the singer/lyricist/composer will usually appear in the ENDING credits [note: song title is never displayed]

use the above and the following common chinese characters appearing in the credits to help you locate what you need to take a screen shot of:

(theme song)

("series head" or opening theme song)

(sub song)

("series tail" or closing/ending theme song)

(music composed by)

(words composed by)

(thanks purin4 for providing several of the translations)