I am planning to trim our budgies nails, they are long enough now to do this. Can I use a sharp nail clipper while someone holds them in a soft cloth?
The talon of the budgies grow continuously but they are normally filed regularly by the movements of the bird on its perches and on its toys. It is therefore necessary to have adapted perches such as perches made of natural wood or therapeutic perches made of cement or concrete (found in pet shops). If you decide to use these abrasive perches, be careful that it does not hurt the inside of the legs of the bird in the long term (these injuries are called "podagres" in birds of prey).
If the length of the claws becomes still very long then I think it is better to ask your vet if it is the first time and ask him to show you how. The technique most often used is to wrap the bird in a towel as you said, and place the bird on the back to gain access to the legs without the budgies can struggle (and by the same opportunity to get hurt). You can use a nail clipper for human being careful to cut only the tip of the claw because talon have blood vessels in the center that can bleed a lot if cut. If this happens, stop bleeding with a haemostatic product (or flour).
So normally there is no need to cut claws in budgies, but only to use good perches. However, if the length of the claws of the parakeet exceeds a quarter of a circle then claws can be cut (1. Ask your veterinarian's advice if it's the first time 2. By following the procedure above).
Budgies that have the nails too long regularly despite the adapted perches, it is better to cut the talon more often to avoid bleeding. Indeed, the vein lengthens with the claws so cutting regularly will decrease its length.
It is best to use a hygienic nail clipper and adopt to cut claws.