“How the cow ate the cabbage” means to tell everything (“straight talk”), like the cow eats everything. Ann Richards (then Texas State Treasurer) used “how the cow ate the cabbage” in a speach before the 1988 Democratic National Convention.
 
“How the cow ate the cabbage” appears to be a thoroughly Texas phrase and is found in print from at least 1935.
 
 
All Things Southern
Once upon a time, a circus came to a small rural town. While they were putting up the big top, a baby elephant escaped and found his way to a little old lady’s garden up the road. The lady in our story couldn’t see very well, but she was alarmed enough to call the police and report a cow in her cabbage patch pulling up her cabbages with his tail. The policeman on the other end of the line listened patiently, “A cow is eating your cabbage, ma’am? We’ll send someone right out.”
 
“I never said he was eating ‘em,” the lady said.
 
“No?” The policeman replied. “Then what is he doing?”
 
The woman hesitated and then exclaimed. “You wouldn’t believe me if I told you!”
 
So, there you have it porchers, now you know why telling someone how the cow eats the cabbage can precede a very serious discussion.
   
Google Books
You All Spoken Here”
by Roy Wilder, Jr.
Athens, GA: University of George Press
1998
Pg. 79:
I’ll tell you how the cow ate the cabbage—stalk and all: Euphemism for President Carter’s threat to whip Senator Kennedy’s ass. 
   
(Dictionary of American Regional English)
cow ate the cabbage, tell one how the v phr
To speak one’s mind; hence adv phr like the cow ate the cabbage with firm or harsh words.
1965-70 DARE (Qu. JJ22, To express your opinion—for example…“I went to the meeting and ___”) Inf TX75, Told ‘em how the cow ate the cabbage; (Qu JJ35b, Other expressions…when you…are just about ready to tell somebody what you think) Inf TX81, Tell him how the cow ate the cabbage; (Qu. LL27, Words meaning “thoroughly”; “The boss bawled him out ____”) Inf OK45, Like the vow eat the cabbage.
 
27 October 1935, Abilene (TX) Morning Reporter-News, pg. 15, col. 3:
Gib Sandefer telling an athletic type fellow just how the cow ate the cabbage.
 
3 February 1937, Port Arthur (TX) News,pg. 12:
So after Albert reached for a magazine for Elmer, the dejected stooge, I told him how the cow ate the cabbage.
   
27 March 1940, Austin (TX) Statesman, pg. 16, col. 2:
...and if you “cross” him, he will tell you how “the cow ate the cabbage.”
 
27 September 1978, Chicago (IL) Tribune, pg. B4:
He says that when Carter last October accused the oil industry of seeking “the biggest ripoff in history,” he praised Carter for telling the country “exactly how the cow ate the cabbage.”
   
1 March 1979, Los Angeles (CA) Times, Letters, pg. D4:
It’s time Uncle Sam got up off his knees and showed a little guts, and told all these two-bit countries how the cow ate the cabbage.
   
8 April 1985, Los Angeles (CA) Times, “Tax Reform Moves to Realm of Possibility” by Jody Powell, pg. C5:
Every one of those segments is well presented in this town by people who don’t have to be told how the cow ate the cabbage.
   
21 March 1986, New York (NY) Times, pg. A6:
When the defendants come to court, Mr. Tigar said, “we’ll show how the cow ate the cabbage.”
 
19 July 1988, New York (NY) Times, “Networks Try Creating Their Own Excitement” by Walter Goodman, pg. A19:
“Cow Ate the Cabbage”
At about 9:30, Ann Richards, the Texas State Treasurer, appeared and began her keynote address. She came out in favor of Social Security and fair play and against AIDS and George Bush. Convention audiences have a way of behaving like a laugh-and-applause track, and this one responded especially to the stylishly got-up woman’s well-polished down-home lines, like “We’re gonna tell how the cow ate the cabbage.” Well, Democrats will do a lot to win Texas.
 
19 July 1988, New York (NY) Times, “Transcript of the Keynote Address by Ann Richards, the Texas Treasurer” pg. A18:
They talked about war and Washington and what this country needed—they talked straight talk, and it came from people who were living their lives as best they could. And that’s what we’re gonna do tonight—we’re going to tell how the cow ate the cabbage.
 
23 August 1988, Washington (DC) Post, Erma Bombeck, pg. E11:
“I think I figured that one out,” I said, “but what’s ‘The cow ate the cabbage’?”
 
“C’mon, you’re kidding. It means those are real facts.”
 
17 April 1990, Washington (DC) Post, “Yawning in America” by Richard Cohen, pg. A25:
The rest of the speech, the part that so endeared Richards to her audience, was made up of Minnie Pearl one-liners (“The sow ate the cabbage”) and the evocation of her own family, a granddaughter named Lily.