I personally take mine to the vet - because I don't want them to be mad at me!! My daughter takes her 'tiel to a pet store
where they charge $5 - I think I pay $10 each for nails and wings. If you are the least bit unsure about doing it yourself, call around and price shop. Make sure to ask if the vets charge an office visit too for that, because that can pump up the price.
My first African Gray got out of her cage and flew straight into a mirror. I thought I'd lost her; she even seemed to be in agonal breathing so I stuck her cage on a heating pad
, covered it up and put the whole thing in my toasty warm laundry room. She was fine the next day, but I took clipping her wings on myself and she looked like she was wearing a bolero jacket for MONTHS.
Be careful - and like Dena said, watch out for those blood feathers! They are both painful and dangerous.