The other answer is good but there are some important things to note about when, how and why should be done if you decide to clip your birds wings.
Why
Clipping of the wings is usually done to either as a safety precaution to prevent the bird from hurting themselves while indoors, or it may be done as an attempt to pacify a difficult or aggressive bird and encourage them to be more sociable and easier to handle. Many pet birds, especially larger ones like parrots achieve flight through speed and may not be able to break away or change momentum quickly enough to prevent running into walls or windows which can lead to injury.
How
Flighted birds have two sets of flight feathers, primary and secondary. Secondary feathers help with maneuvering and gliding and also support maintaining flight. Primary flight feathers are longer and towards the end of the wing. They are crucial for the bird to take off and achieve vertical lift.
When clipping be sure to only clip the primary feathers and never clip them below half of their original size. If done properly it is not painful for the bird and they should be able to still safely glide or fly downwards without falling. They may still fly vertically but it should be very exhausting for them to do so, discouraging too much dangerous flight activity indoors.
Above shown is a chicken but the process is the same
Generally to get the bird ready to clip you should pick them up gently with a towel and attempt to cover their face so they can't see. It is less stressful for the bird when done quickly and gently. If you are unsure then it is best to consult a veterinarian for assistance or for instruction in how to perform this procedure in your home.
Be careful to hold their head steady, they don't generally like this and get a little bitey!
When
It is crucially important not to clip a birds wings until a good time after they have been fledged. Learning to fly is one of the most crucial parts of a birds development and doing this at too early an age can have serious and permanent developmental affects on the bird physically and psychologically. They may have poor development of breast muscles that prevent proper flight as adults, and in other cases may have psychological and confidence issues, or may have difficulty bonding with humans or other birds.
When purchasing a flight bird as a pet, ensure that the breeder or pet store owner allows the bird to be fully weened and have a good amount of time to master flying before they clip wings. There are many breeders and pet stores only concerned with money and not with the animals well being.
When clipping also check for swollen or infected blood feathers as they may be more common. Sometimes a fall or an accident can cause a clipped feather to start to bleeding then it very well may not stop on its own, in which case it is highly important to seek immediate assistance from a veterinarian or pluck the feather yourself if you are comfortable doing this.
Other Important Notes
Pet birds that have been clipped tend not to get as much exercise as they would normally get in the wild (barring domesticated birds like chickens). It is important they get extra mental stimulation and physical exercise to prevent too much muscle loss.
Remember that birds molt periodically (frequency depends on the species), so clipping flight feathers is not a permanent change. Allow new feathers to grow in fully before clipping again. When the feathers are still growing, they have active blood vessels in them. Trimming these blood feathers' can cause the bird to lose blood. If the bird happens to be bleeding from a cut blood feather and you cannot stop the bleeding, then plucking the damaged feather completely will generally help it stop. If you are not comfortable doing this or you are unable to then consult a veterinarian immediately! You can identify a blood feather by noticing the dark or red colour part way up the shaft of the feather from the skin.