FORMAL: The American Sign Language (ASL) sign for "formal"

The English word "formal" can be expressed in ASL as the sign "FANCY/POLITE"

If you mean formal as in dance or ball you could sign DANCE or fingerspell FORMAL + DANCE:

If you are referring to PROM, you can use the sign for PROM or fingerspell:

Notes: 

Also see: CELEBRATION

APPROPRIATE

PRECISE

DANCE