I never met a cat (of any age) who COULD NOT be
trained, just owners who WOULD NOT.
Yes, it does take time to learn how to trim nails correctly and you do have to make an effort to train, but, while some cats present more of a challenge than others, it CAN be done! (And YOU can do it!)
Ask questions; assess a variety of approaches if the first
ones you hear about don't seem like they'd work in your
own situation; once you determine what method you and
your cat will use, BE CONSISTENT!
Get your cat accustomed to having you touch its paws. Decide where you will do nail trimming; you will need to have a good source of light and you will want to be able to gently, but firmly, control your cat.
Hold the cat as you later will for trimming, but just gently examine the nails on each foot for a moment. Then immediately reward the cat. Do this a number of times until your cat is at ease before you do the manicure, itself. You want your cat to be very relaxed and comfortable with this activity before you even consider trimming nails.
You may want to have a partner for manicuring, so that one holds, and the other clips. Depending on your cat, this may be easier, although some cats do best when distractions and activity are minimized.
You may want to initially do only one nail at a session. By rewarding your cat immediately following that single snip, you'll increase your cat's willingness to participate. After a few "quick clips", you'll be able to do additional nails in a single session and your cat will be reasonably calm and accepting (since it will know that it has nothing to fear from the experience).
Get a pair of clippers or nail trimmers designed specifically for cats; look for a well-made product. If you've ever tried to use dull or misaligned clippers on your own nails, you'll know why you want to invest in a GOOD pair! Ones made from surgical steel may be a bit more expensive but will tend to stay sharp and do an easier, more efficient job of trimming. There are a number of types; hold each and determine which would be most comfortable for you to use and easiest to control and manipulate.
If you are at all unsure of how to correctly trim nails, it would be good to observe an "expert".
Ask your vet, a pet groomer or someone else with experience to demonstrate (a local breeder or animal shelter may be good places to check). You want to be certain that you know how to correctly
extend the claw without causing discomfort to your cat by pressing too hard.
It's also useful to be able to locate the vein inside the claw. (You want to stay well away from it to avoid great discomfort to your cat and a shower of blood!) When in doubt, trim only a tiny bit from the very tip.
Determine when and where the "bad" behavior occurs.
Provide an appropriate alternative that is inconsistent with
the "bad" behavior (for example: A scratching post instead
of the couch; a toy instead of human flesh).
Discourage "bad" behavior when you are present (water from a
spray bottle or squirt gun; noise from shaking a can of pennies;
loud "OUCH!" if personally 'attacked', etc.).
Prevent "bad" behavior when you're out (eliminate
temptations by keeping the cat in a cat-proof area or by
covering 'desirable' furniture or carpeted areas with plastic
or other materials).
Praise "good" behavior (using the scratching post or
playing gently, etc.).
Finally, BE CONSISTENT:
Don't permit undesirable behavior "sometimes". Be clear what you will and will not allow and make sure that everyone in the household (including your cat) knows, and follows, the same rules.
Behavior modification techniques are very powerful and will work with your cat if used correctly.