So sorry to hear about Tom. He does sound like he is nearing the end im afraid. Don't be fooled by the purring - sorry but this is very common in ailing cats, especially if it is loud .
I used to be a vet nurse so have been through this many times, its still heartrending. I have to say, children are pretty resilient although i wouldn't tell them until afterwards. Just say that he is going to the vets as he is very very old and poorly. Then just tell them that he has passed away - allow them time to say goodbye but don;t make a big drama of it, just say he is going to the vets now - to give him a cuddle before he goes.
What you need to do is phone up your vet and make an appointment. It is often better if you can tell the receptionist over the phone. Just helps to have everything ready. You can stay with Tom if you want to - i always recommend that owners do this as there are no questions unanswered. What will happen is this - the vet, aided by a nurse may or maynot shave a little bit of fur from Toms leg - just to make access to the vein easier. He will then be given an injection into the vein which is basically an aneasthetic overdose - he will drift off to sleep just like he was having an op. It is all very quick and painless for kitty.
Some people decide to have their pet's ashes returned to them, it is worth considering this before you go, but you can phone the vets after and let them know if you need time to think. I have my dogs and my rabbits (all upstairs in boxes as i have never been able to scatter them!) and it helps as i feel they are close to me still! Otherwise they go to the crematorium and are cremated with other cats (just cats) then the ashes are spread en masse and the fields often planted over with grass, daffodils etc.
Sorry, this is all a bit factual, but i always feel it is good to be prepared.
It is a terrible, gut wrenching decision to have to make, but I have never ever doubted any euthanasia that i have assisted in, i have always felt that it has been the right thing to do for the animal.