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Use a very long circular needle. Choose the stitch and pattern of your preference. Choose the scarf length. Cast on. Knit around and around. Continue knitting until it reaches the height you'd like.
If you use a small one, you'll only knit enough to make a cowl, which is a short infinity scarf but you won't be able to wrap it again and again. The needle size should be at least 4mm/6 US and above. Knit stitch works well for beginners––knit even rows, purl odd rows. You can vary the number of rows as you go. You'll need to gauge the final length from the stitch used by making a sample piece of about 15 stitches and measuring its gauge. This tells you how many stitches fit for each 5cm/2 inches, allowing you to calculate the final length desired. Using your calculation from the previous step, cast the number of stitches needed for the required length. Then connect the beginning and end of the row and start knitting in circles.  Then cast off and the infinity scarf is complete.