Summarize this article:

After you've strained the martini into the glass, twist the lemon strip that you cut over the glass to express the oils. Next, rub the peel along the rim of the glass. If you plan to use olives as a garnish in place of the lemon peel, place one or two on a toothpick to ready them. Once you've rubbed the lemon peel around the rim of the glass, make sure that it's still twisted. Drop it into the martini so it floats in the drink. If you're using olives instead, place the toothpick with them on it into the glass. They won't float, so you may want to hook them on the rim. If there is any excess martini left in the shaker after you strain it for serving, strain the remainder into a regular glass. Place the glass in a bowl full of ice so it will remain chilled until you're ready to drink or serve the rest.

Summary:
Express the lemon strip over the glass and rub along the edge. Float the peel in the martini. Strain the excess martini mixture.