There are two ways to knit an armhole in a sweater. The first is from the bottom up, and can be used to create a space in which to set a sweater sleeve or to create an sleeveless hole for a vest or tank top. The second is knitted from the top down, incorporating the top of the sweater sleeve in the process. Sweaters made in this way are called "raglan." Both methods have their merits.
Knit the body of the sweater from the bottom up to 3-inches below the armpit. If knitting the body in the round, divide the total stitches by 2. Count off half the stitches, and place them on holders for the back. Tie yarn markers at each end to mark the bottom of the armhole. Divide the remaining stitches by 2, and mark the centre front with a yarn marker to facilitate shaping the neck.
Place all the stitches for the front on one needle. Slip the first three stitches onto a yarn holder. Knit across the work from right to left, with the right side of the work toward you. Slip the last three stitches onto a holder. Turn the work, and purl across. Turn the work, slip one stitch, knit one, then pass the slipped stitch over the knitted stitch. Knit across, and knit the last two stitches together.
Knit the sleeve edge in this manner until it has curved in sufficiently to allow good arm movement or until it matches a standard shirt sleeve pattern. When you reach desired placement for the bottom of the neck, divide the front stitches by two. Place half the stitches on a holder while you continue shaping the sleeve and begin shaping the neck.
Increase the rows when you reach the last six rows before the shoulder by knitting across to the last stitch of each knitting row, then putting the needle through the yarn between that stitch and the next, and pulling a thread through to form an added stitch, then knit the last stitch. Turn and purl across, continuing to the top of the shoulder. Place the shoulder stitches on a knitting holder.
Complete the other half of the front in this same manner. Work the decrease stitches for the back in the same way as the front, but do not place added stitches on a holder at the arm pit, unless the person has especially large or muscular arms. The ending number of stitches at the shoulder seam should be the same for front and back.
Weave or crochet the shoulder seam stitches together. Finish the armhole by slipping the stitches off the holder onto a circular or double pointed needle. Pick up stitches by pulling loops through the ends of each knit row, and holding them on knitting needles. Knit four rows of ribbing onto the armhole for a sleeveless sweater, or knit a sleeve onto the sweater.
Knit the sweater collar on a circular needle or on double pointed needles, starting from the top edge. When the neckline is reached, divide the stitches into front, back and shoulder tops. Mark the divisions with contrasting yarn loops or plastic knitting markers slipped onto the needles between stitches.
Calculate the number of stitches for each part in the follow manner: Multiply the number of stitches per inch from your knitting gauge by the inches around the person's neck for the neck stitches; multiply the total stitches by .33 to get the number of back stitches, and multiply the number of back stitches by .25 to get the number of stitches for each sleeve. The remaining stitches will be front stitches.
Increase stitches every other row, beginning with the first knit row after completing the collar. To make the increases, yarn over when you come to a marker, slip the marker, knit one and yarn over again, and continue knitting to the next marker. Do not increase on the following row, but do slip the marker when you come to it so that you do not lose track of the pattern.
Knit the increase rows until the sweater reaches at least 2-inches below the wearer's armpit. Some people may prefer a larger sleeve, so you may want to knit a few more rows. Place the sleeve stitches on holders and knit without increasing to the tail of the sweater. Finish as desired.
Return to the sleeves. Knit a short row of ribbing to create cap sleeves, or knit long sleeves onto the sweater, finishing with a traditional ribbed cuff.