To open his mouth, sit on the floor with him between your legs facing away
from you, so when he backs up, he can only back up into you.  grab his head
across the top, just behind the eyes, and hold the cheek bones.  lift his
nose up towards the ceiling.  once his nose is pointed at it, his jaw will
naturally open slightly.  use your other hand to slip a finger in on the
small teeth in the front between the canines.  If your kitty fights you, you
can slip one of your other fingers (from the hand holding the cheekbones) in
and take a small piece of his lip with you, to wedge between your finger and
his teeth, so when he starts biting down it hurts him.    If your just
checking his teeth, you can put your finger on the corner of his mouth and
pull back slightly, then lift up the rest of the lip.  Hard to translate
into words.. the key is to make the holding of the cat easy and stress free
for the kitty so he doesn't start fighting you till you start doing
something.  Praise him after every single attempt, and give a treat.  You
should start doing these things now, so when the time comes when you HAVE to
do it, its not a stressful event.

As to clipping.  I personally put the kitty in my lap, on his back, and use
arms and elbows to pin the cat in the position I want while trimming.  I
give lots of cuddles and kisses, so it seems a lot like a bad cuddle
session.  At work, I put the cat on the table, put my arm around the kitty's
chest, so the head is hanging over my arm, and work on one leg at a time.
again cooing and nuzzling the kitty from behind.  If the cat is obnoxious, I
have the owner coo as well.  You only have the back feet to do, so it should
be half as difficult.  however if you've never done it, start by just
playing with your kitties feet.. getting the claws to extend, and holding
them out for longer and longer periods, all while cooing and praising your
cat.  You'll need to hold them out for 10 seconds or so while you prepare to
cut, so in practice, work for that amount of time.   Cats nails are just
like fingernails only in a different shape.  It does not hurt to cut them,
but if you cut the quick (the pink stuff in the middle) the kitty will
bleed.  no biggie for the cat, but mess for you.

Good luck.