The English word "big" is a little three-letter word, but there is a big number of ASL signs in American Sign Language (ASL). Plus, some signs can be inflected. They are not always interchangeable.
For a starter for beginners, this is a basic ASL word.
Meaning: Of considerable size, number, quantity, magnitude, or extent; large; huge.
Pronunciation (sign description): Two flat hands apart in neutral space, palms facing each other, briskly diverge from each other.
Usage/context examples: "my puppy grows bigger and bigger" (be sure to inflect the ASL sign for "bigger and bigger").
Pronunciation (sign description): Two "clawed-L" hands apart in neutral space, palms facing each other, diverge from each other.
Usage/context examples: "a big house in the country",
Pronunciation (sign description): Two "clawed-L" hands apart in neutral space, palms facing each other, diverge from each other in a slightly arc motion. Also means LARGE.
Usage/context examples: "a big decision".
Meaning: grown up.
Pronunciation (sign description): Dominant bent hand held in right-sided space at about the neck level moves in a slightly arc motion toward the higher space at about the head level.
Usage/context examples: "you're a big girl now".
Pronunciation (sign description): Dominant horizontal "big-G" or "clawed-L" handshape held in space with a firm movement.
Usage/context examples: "you should write April with a big 'a'" (capital).
Here are some other signs and/or classifiers for other phrases other than the ASL words above.
Use classifiers for such these phrases as: "big hazel eyes", "a big toe".
Use verb inflections for such phrases with no "BIG" in ASL translations as: "She's always been a big spender" meaning "she has always spent a lot of money" (glossed in ASL as "IX1 ALWAYS TEND-ma 2h-SPEND++th").
Meaning: older or more like an adult. "Her big (= older) sister/brother teased her so much". Use OLDER in ASL.
In English, "big" is sometimes used to mean "to be important or famous or popular", use IMPORTANT, FAMOUS, or POPULAR.
Related signs: HUGE, LARGE, ENORMOUS, GREAT, GIANT, MASSIVE.
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.