Here's a pattern for the quick little tea cozy. It took me about an hour and a half to finish and it's great for using left over cotton yarn.
Notes - The entire body of the pieces is worked through the back loop only (this is my first pattern be kind)
Chain 30 sts
1st row: DC in 2nd chain from hook and in each chain to end of row. Chain 2 Turn
2nd Row: DC into each DC to end, Chain 2 Turn
3-15: Repeat 2nd row
16th Row: DC into first 15 DC, Chain 10, Skip 10 DC, DC into last 5 DC
17th Row: DC into 5 DC and DC into each chain stitch, DC into last 15 DC, chain 2 turn
18-31: DC into each DC, Chain 2 turn
Take piece and whip stitch first 6 stitches together skip the next 18 stitches and whip stitch the last 6 stitches together. You should now have a tube with openings on either end.
Contrasting border is worked through both loops
With contrasting color chain 35 sts, cut yarn and place chain to the side
With contrasting color sc into each SC 2 times to form a contrasting border cut yarn.
With contrasting color SC into each DC on one side in the opening that was not sewn together (10 DC) SC in where both sides of the opening meet. SC into each DC on the other side (10 DC) SC into opposite end where the sides of the opening meet. Cut yarn
Weave in loose ends
Take the Chain 35 and weave it into the 5th row from the top and pull to gather top as needed
I know this isn't the clearest pattern but if you have any questions leave a comment and I will gladly walk you through any issues.