Before eating, いただきます【itadakimasu】 is often said. The word simply conveys thankfulness when receiving something. It can be used when receiving from anyone, whether a teacher, God, or your next door neighbor. In other words, there is no direct religious connection.
If I'm in a meeting and the host offers me a doughnut, in Japanese I'd say いただきます as I take it from the plate. In English, I'd say, "Thank you."
You might come across a few other phrases used when eating, but I'm not aware of any with direct religion connotations.
Other example uses of the word:
これをいただいてありがとうございます。
【kore wo itadaite arigatou gozaimasu】
Thank you for giving me this. (In English it conveys both the thanks and the fact that "this" was given to you.)
先日、手伝っていただいてありがとうございます。
【senjitu, tetsudate itadaite arigatou gozaimasu】
Thank you for giving me a hand the other day.