For this elephant I used worsted weight yarn and an E/4 hook.

Step 1: Body

Row 1: Magic ring, 6 sc (6) Don't cut the end of the yarn off
Row 2: inc around (12)
Row 3: inc, sc around (18)
Row 4: 2 sc, inc (24)
Row 5: inc, 3 sc (30)
Row 6: 4 sc, inc (36)

Pull the tail out by poking the needle through the magic ring and pull the end of yarn out.

Row 7-14: sc around (36)
Row 15: dec, 4 sc (30)
Row 16: 3 sc, dec (24)
Row 17: dec, 2 sc (18)
Row 18: sc, dec around (12)
Row 19: dec around (6)

Fasten off. Weave loose end through each stitch in the opening. Pull tightly to close.

Step 2: Head, Ears, and Legs

Head
Row 1: Magic ring, 6 sc (6)
Row 2: inc around (12)
Row 3: sc, inc, 2 sc, inc, sc, inc, 2 sc, inc, 1 sc, inc (17)
Row 4: 1, inc, 3, inc, 2, inc, 3, inc, 2, inc, 1 (22)
Row 5: 2, inc, 5, inc, 4, inc, 5, inc, 2 (26)
Row 6: 4, inc, 7, inc, 8, inc, 4 (29)
Row 7: 7, inc, 9, inc, 9, inc, 1 (32)
Row 8: 13, inc, 18 (33)
Row 9: even (33)
Row 10: 18, dec, 13 (32)
Row 11: 1, dec, 9, dec, 9, dec, 7 (29)
Row 12: 4, dec, 8, dec, 7, dec, 4 (26)
Row 13: 2, dec, 5, dec, 4, dec, 5, dec, 2 (22)
Row 14: 1, dec, 2, dec, 3, dec, 2, dec, 3, dec, 1 (17)
Row 15: dec, 1, dec, 2, dec, 1, dec, 2, dec, 1 (12)
Row 16-21: sc around (12)
Row 22: dec around (6)

Fasten off. Weave loose end through each stitch in the opening. Pull tightly to close.

Feet (Make 4)
Row 1: Magic ring, 4 sc     (4)
Row 2: inc around (8)
Row 3: BLO sc around (8)
Row 4: sc around (8)

Ears (Make 2, Use different color)
Row 1: Ch 5
Row 2: 3 sc, inc, ch 1     (5)
Row 3: 4 sc, inc, ch 1     (6)
Row 4: 6 sc (6)
Row 5: 2 sc, dec, 2 sc (5)
Row 6: dec, 1 sc, dec     (3)
Row 7: 1 sc, dec (2)

I used green buttons for the eyes and added a blue button to the end of the trunk.