How to Garnish Cocktails (for Beginners)

Citrus Wheels:
0 Hold the fruit by one end (the base or the top) and slice straight through the middle of the fruit. You’ll now have two halves, each exposing the circular, wheel-like shape of the interior of the fruit.
7 Now, hold each half by its end and cut them into several sections, each about ¼” thick. An average-sized orange will yield about 6-8 perfectly shaped wheels and a few small ones from each end.
8 To sit a citrus wheel on the rim of a glass, cut a slit from one edge of the wheel into its center. Be careful not to cut it all the way through to the other side. Now place the wheel slit-side down onto the edge of the glass.
Citrus Slices:
9 A citrus slice is incredibly simple to master once you know how to cut a wheel. Simply cut each wheel in half and you’ll have two slices!
10 To secure a slice on the edge of your glass, cut a slit into the flesh side of the slice, being careful not to cut all the way through to the peel. Place the slice slit-side down onto the rim of the glass.
Citrus Wedges (Method 1, Simple Style):
11 Hold the fruit vertically and cut through the middle, from one pole to the other. This is opposite of the way we cut a fruit for citrus wheels. You’ll see the curved, half-moon segments of fruit on the inside.
12 Next, remove the top and bottom of each half. Now cut out the thick center pith by slicing down and at a slight angle on each side of the pith. Don’t cut all the way through, just about ¼ inch into the fruit will do the trick. 
15 Hold each half by the rounded side of the fruit (trimmed ends pointing towards and away from you), and slice each into four wedges.
16 To place a wedge on the rim of a glass, cut a slit into the flesh side of the wedge, being careful not to cut all the way to the peel. Use the slit to securely position the wedge in the glass.
Citrus Wedges (Method 2, Fancy Style):
13 For citrus wedge style number two, hold the fruit by one end, like you’re cutting wheels. Slice the fruit in half, then cut each half in half again.
17 You’ll see that one wedge from each half has an attractive side and a side with a lot of pith from the end/pole of the fruit. Carefully trim off the excess pith from those two wedges.
14 You’ll have four beautifully segmented wedges from each side of the citrus. This style of wedge cutting is perfect when you want smaller citrus wedges. Use this method to cut small lime wedges that can be popped inside bottles of Mexican beers.
Citrus Twists:
18 Use a paring knife or a vegetable peeler to remove a long, wide swath of peel. Try not to take too much pith with the peel if you’ll be placing the peel in the drink.
19 Next use your kitchen shears or paring knife to trim the edges of the peel into a rectangle or give the peel a fancier look with angled, pointed ends.
20 At this point, your citrus peel is ready to use. Twist it (or fold the edges back towards yourself) while holding it over the glass, peel facing the drink, and watch as the oils spray from the peel. Run the expressed peel along the rim of the glass for even more flavor and citrus scent.
21 You can discard your peel, place it in the drink, or place it on the rim of the glass. A nice way to enhance the look of your twist is to use a chopstick (or bar spoon handle or similar-shaped object) and literally twist the peel around it. If you place it on the stick like this for a minute or two, it will hold its spiral shape for a surprisingly long time.
22 To place a twist on the rim of a glass, cut a slit about an inch and a half long in the center of the peel, lengthwise. Use the slit to sit the twist on the edge of the glass.