I you mean "I'm going to eat now", it's just future tense in English: eat is the main verb; going is just an auxiliary verb that provides the tense. Since Japanese has no future tense, you just use the main verb.
これから、食べる【たべる】
korekara, taberu
If you mean "I'm going [somewhere] to eat", it's a little different. In this case going is the main verb.
これから、食べに行く【たべにいく】
korekara, tabeni iku
Explaination
First case: Japanese doesn't have a future tense. In English we say "I'm going to ..." or "I will ..." In Japanese, you just use the regular present/future tense, and use other words like これから if it's not clear from context that you're talking about the future.
Second case: To say that you are going somewhere to do something, you put the action verb in 連用形 (i.e., ます form without the ます: e.g., 食べ, 切り, etc.) add に and then 行く.
Other examples of the second case:
魚を買いに行く
【さかなを かいに いく】
sakana wo kai ni iku
I'm going to buy fish.
ガス代を支払いに行く
【がすだいを しはらいに いく】
gasudai wo shiharai ni iku
I'm going to pay the gas bill.
Note that there are fairly literal translations and sometimes it'll be more natural to say it using other words depending on the situation.