Before you trim
Start off stroking your pup’s legs and paws. Always start by stroking in an area he enjoys, such as his sides or neck. Then, every once and a while, stroke his side then run your hand down his leg to his paw and then resume stroking his side. Feel free to slide him a treat (or have a friend give him a treat) if this is helpful and doesn't cause him to become too excited and active.
When he is relaxed about this add in some toe touching, a little at a time, mixing plenty of warm words and regular stroking into the mix. If your pup has no complaint, gently press his toe, give him a treat, praise and go back to regular petting. Practice this for several, short sessions instead of one long one as many pups become fussy at too much of this sort of thing.
Once your pup allows you to handle his toes with ease, take your pup nail clippers (ask your veterinarian or groomer which type is right for your pup). Stroke the clippers against his toe, praise, give your pup a treat and put the clippers down. Go back to regular petting. Repeat until he shows no hesitation about being touched by the clipper. If you handle his feet and toes daily as part of your normal routine he'll lie with his feet happily in the air next pedicure time.
Trimming your pup's nails
Nip the very end of his nail off. On white nails this is fairly easy to see. If your pup has dark nails or if you're worried about what to clip, ask your veterinarian or veterinary technician next time you're in the office for puppy shots. Try to stay relaxed, as your pup will pick up on any tension. Keep your hands and your voice calm.
When you start to cut his nails, don't try to get them all cut at once. Snip one, belly rub for a while, snip another. If it takes you two or three sessions to get all your puppy's nails trimmed that's okay. This is not a race.
You can apply this same general technique to other grooming tasks such as ear care or brushing. Just follow the basics: start at a place your puppy enjoys and then slowly introduce the new procedure. Make it pleasant and full of rewards and your pup will soon be accepting it with no fuss at all.
This is well worth an investment in time and patience now since the pay off is a decade or more of easy, no stress handling for both of you.