Answers

Step 1:
There is a card trick called Pairs Repaired, or Mutus Nomen Dedit Cocis. The basic idea involves having 10 distinct pairs of letters in four 5-letter words, such that any combination of two rows (not necessarily distinct) has exactly one duplicated letter. Filling in the blanks, we get:

CRACK BONGO LAPEL FUGUE
TRYST DINED SOUPS MIMES
APPLY BRIAR UDDER HOOFS
LOOKS GAFFE TAROT TIGHT

CLOCK FIFER CROON YELLS
ANNUL TRUST APNEA HOOTS
BUSKS MEMOS CELLS RATER
MAMBO UNION USURP HAPPY

The new letter added to each box gives COLUMNUP. "Column Up" perchance? This clue tells you to look up the columns to find new words.

Step 2:

TRYST DINED SOUPS MIMES
APPLY BRIAR UDDER HOOFS
LOOKS GAFFE TAROT TIGHT

CLOCK FIFER CROON YELLS
ANNUL TRUST APNEA HOOTS
BUSKS MEMOS CELLS RATER

You get SNOOPY, MUFFIN, CACTUS and RHYTHM. It's the same process all over again, only with 6-letter words this time! You get the letters P, I, A and R. That can only give PILLAR, which is a COLUMN that holds something UP.