Worms can be purchased from the main menu --> customisation --> my worms/ my formations.
The first worm of each class costs 80 coins, the second 160 coins, the third 240 coins and the fourth 320 coins. In total you'll need 2400 coins to purchase all 4 worms in all worm classes.
You gain coins by completing campaign and puzzle missions. Depending on the medal you win (gold, silver or bronze) you receive between 20 and 80 (in some levels even 140) coins. The faster you complete a campaign mission the more coins you'll get.
For 2400 coins you'll need to complete approximately 2/3 of the single-player missions. If you're having trouble you can also download the DLC add-ons for the game to gain extra coins. The Funfair-Pack includes some easy puzzles for example.