I’m not Religious (Atheist), but I was brought up in C of E schools and had to say Grace at every mealtime.
I heard it on TV the other day, and immediately my brain said ‘WRONG’.
What I am used to saying is…
“For what we are about to receive, may the Lord make us truly thankful”
What I heard was…
“For what we are about to receive, thank God”
Is there a ‘correct’ way to say it?
Short version: No.
The prayer you say over your food can be completely different from one person to the next; asking if there’s a correct way to say it is kinda like asking if there’s a correct way to pray.
When Jesus’ disciples asked Him that question, He handed them the Lord’s Prayer, which isn’t rules but more like…guidelines. 
Anyway, “Grace” over food can range from the Thanksgiving table patriarch’s seemingly endless list of things to thank God for this year, while stomachs furtively rumble, to variations on the rote version that you learned, to the small child’s simple “Thank you god for this food amen”, which is what I taught my kids.
…and bless the cook.
It can even be a song. At church camp we sang Johnny Appleseed.
“Come Lord Jesus be our guest, let this food to us be blessed. Amen.”
“Rub a dub dub, thanks for the grub.” merited a rap on the knuckles.
According to wikipedia, “For what we are about to receive, may the Lord make us truly thankful. Amen.” is a common form of grace in English schools.
Wikipedia has a list of examples from various faiths and traditions. I kind of like the Scots one.
And there’s always “Rub-a-dub-dub, thanks for the grub, yay God!”
ETA: Curse you, Squink!
For my family it’s always been:
Or the Latin version we had at school:
Johnny Appleseed is positively pious compared to some versions we sang at Girl Scout Camp. I’ve sung grace to the tune of the Flintstones theme song and the Addams Family theme song to name two popular tunes.
That said, although Duck Duck Goose is correct, there may be a standard form which was said in the C of E Schools Lobsang went to, and if that has been tweaked, I can sympathize with feelings of startlement.
“2 4 6 8, dig in, don’t wait!” Agnostic – the religious side of the family don’t get me to do grace. 
As do I… should I find myself requested to say grace I think the Selkirk version would be fun.
My little brother’s version when he was about 5 or so:
“God is good, God is great. Let us thank him for this food. Amen, and thank you, God!”
That grace makes it rain, so in some situations it is wrong to sing it, or at least impolite.
Thank the lord who made us able to enjoy what’s on the table.
If there’s more still in the pot, bring it on while it’s hot.
but really…
My family’s grace is always improvised “We’re grateful for the good food we’re about to enjoy, and that Sally and Tim made it to town before the snow closed the airport. Before we eat let’s remember absent friends.” Never the same from meal to meal, and typically only said aloud at big family meals. Several of us who are religious (about 50% of my family) pause briefly before each meal, but it’s private.
the shorter answer would be, No, there is no one “correct” way to say grace.
Or the ever popular, “Good bread, good meat, good God, let’s eat.”
Since there is no correct single answer here, let’s move to IMHO.
samclem Moderator, General Questions
If you modify your first example slightly, it can work even for non-believers. “For what we are about to receive, may we be truly grateful [or thankful].”
I’ve never heard this anywhere else, but it’s what we said when I was young:
“Our hands we fold, our heads we bow
For food and drink we thank thee now. Amen”
My standard grace isn’t any set prayer. I try to start by thanking God for the blessings of the day, particularly the food I’m about to eat. I ask God to bless the food so that it may nourish me to do God’s will. Then I finish off with a “I pray this in Jesus’ name. Amen.” If something special is happening, I’ll throw that in too. On occasion during a silent grace, I start with actual words in my mind and drift off into just sitting with the Lord, feeling thankful. I figure that God knows what I mean.
I have a friend who is a very conservative Catholic and this is his preferred grace before meals.
And for the republic for which it stands, one nation, under God, with liberty and justice for all…oh, wait…that isn’t the same thing.
(that was ours as well, raised Catholic)
Wait.
People have set phrases they say when they say grace before a meal?
My family and friends have always just prayed. We just pray whatever we are thinking or feeling is relevant, usually including thankfulness and so forth.
Is my experience unusual?