It is best to watch someone else do this before you do it on your own because doing it wrong could lead to a significant bleeding and possible death of the budgie. Your avian vetrinarian or another bird owner or breeder would be good choices to demonstrate this procedure for you.
Before grabbing the scissors, make sure to have the correct supplies ready just in case you snip a bloodfeather: a pair of tweezers or needle nosed plyers, styptic powder (like KwikStop), and cotton balls. You might also need a towel with which to hold your budgie if he or she is a biter.
The picture marks the primaries which are the feathers you want to trim. It is important to check the underside of the wing feathers for any visible blood feathers. If you see any, do not trim those feathers. You should trim the primaries up to the second layer of feathers on the wing.
If you do accidently cut into a blood feather, immediately apply direct pressure to the bleeding area. If after a few minutes it has not stopped bleeding, apply styptic powder to a cotton ball and press it against the feather shaft. If this does not stop the bleeding you will need to pull the blood feather. To do this, use the tweezers (or needle nosed plyers) and gently pull out the entire feather. Then apply direct pressure to the follicle until it stops bleeding. If all these methods fail, keep applying pressure and take the bird immediately to an avian veterinarian.