To make Poliwhirl evolve into a Poliwrath, give it a Water Stone.
To make Poliwhirl evolve into a Politoad, you have to make it hold a Kings Rock and Trade it to a friend. Than make them trade it back.
Poliwrath is better than Politoad because it has better Attack and better Defense. It also is part Fighting type!
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Use A Leaf Stone
You can either give it a water stone to evolve it into Poliwrath, or trade while it's holding a King's Rock to evolve it into Politoed.
A Kings Rock can be used to evolve a Slowpoke to a Slowking, a Poliwhirl to a Politoad or a Seadra to a Kingdra. Note, you have to trade these Pokemon while they are holding it to evolve them.
Currently only two Pokemon evolve when traded while holding King's Rock. These two Pokemon are Poliwhirl and Slowpoke. Poliwhirl evolves into Politoad and Slowpoke evolves into Slowking.
Go to Cerulean City, and go to the house next to the Pokemon Center. Talk to the old man and he will trade his Jynx for your Poliwirl. *Your Jynx will be the same level as your Poliwirl.