Krabby was caught by Ash near Bill's Lighthouse during the sunset. Ash did not use a Pokémon to capture Krabby, instead he just threw a Pokéball after throwing a stick at it.
Being Ash's 7th Pokémon, Krabby was transferred to Prof. Oak's laboratory where it stayed and enjoyed some of Prof. Oak's poetry.
Kanto Pokémon League.
Ash's first battle in the Indigo Plateau was on the water field and Ash decided to call upon Krabby to help him out despite not having any battle experience so far.
Krabby was Ash's first choice Pokémon against his opponent, Mandi, who was using an Exeggutor. After becomming trapped in the pool due to Exeggutor's Psychic attacks and looked to be in trouble as Exeggutor then started to bombard the pool with an Egg-Bomb attack.
A concerned Ash attempted to recall Krabby but the whirlpool prevented him to do so. Krabby however, managed to turn the battle after regaining its composure and managed to clamp onto exeggutor with a vicegrip attack. With the battle advantage in Krabby's favour, he managed to beat Exeggutor after a Leer and Stomp attack.
After the battle Krabby evolved into Kingler which was caught live on camera and seen by the audience.