Put food into the mouth and chew and swallow it.
Same sign for FOOD. Whether it's a noun or a verb depends on what position this sign is in a sentence.
There are some more synonyms for EAT below.
To put food into mouth using a spoon or a fork (e.g. eating cereal, soup, and such).
To put food into mouth such as eating some popcorn, nuts, or such.
First 100 words.
As you feel more comfortable with the first few hundreds of ASL signs, progress further with your vocabulary and learn signing more.