I am updating this day to day as things come up, or I think of something. I decided to compile it because people seemed to be making fundamental mistakes in caring for their kittens, either through a lack of common sense, or a desire to do the best for their cats without realising the consequences! Nearly all these points have come up through my experiences with Rescuing (I'm the Rescue Officer for the Old-style Siamese Club).
ALWAYS weigh your kittens daily. The first sign of a problem is shown by weights. Even a very experienced breeder cannot judge a weight gain or loss of a few grams overnight or over 24 hours by 'feel' - nobody can, and this could be a first sign of trouble that could be averted. Weighing am and pm is not a bad idea in the first couple of weeks, as that will give you an even clearer idea of progress.
ALWAYS spend time with the kittens to watch their litter behaviour. Some kittens have developmental problems in the urinary system, and a kitten trying to urinate constantly without success will eventually burst its bladder if you don't step in. You also need to watch out for tummy upsets.
Check hydration of the queen and kittens daily (pinch up the fur - if it doesn't snap back but remains standing for a while, the cat is dehydrated and needs veterinary care.) Always keep a couple of sachets of small-animal rehydrations salts in the house (Lectade) as the speedy administration of this can cure early diarrhoea symptoms and save you from extensive veterinary bills if a cat is dehydrated.
Having a kitten room
Most breeders establish a kitten room in their house. This is mostly for their own sanity, but also for sanitation! Kittens need to be confined or they will run wild and become manic. More to the point, they will widdle everywhere. It's very important for litter training that the kittens are surrounded by litter trays, so there is never any excuse for going anywhere else. If you give your kittens a bit more space, you absolutely must not do it until their litter training habits are fixed in place. Even then, there must be litter trays in every likely corner. Don't let them sleep on your bed, as they will wet it, and that habit is extremely hard to break, and may cause the new owners to return the kitten to you.
It is important that the queen can come and go freely but the kittens cannot: put a barrier or half-door in the doorway so that the queen can come and go to find you if she wants, and also so that she doesn't have to be stuck in with her kittens all the time. They get bored, so make sure you take plenty of time to play with her every day.
Although it is good to let your queen have her way about moving the kittens etc., you must have a boundary point at which you will not allow her to have her own way. I had a queen who was determined to put her kittens on top of a cupboard. In the end we compromised by letting her go on top of the filing cabinets in a sturdy box, but when they were older they had no choice but to go into the kitten room where they could learn to run about safely.
Although a kitten room puts a certain distance between you and your babies, this can be a good thing: letting them go to their new homes is hard, and having them in their own room reminds you that they are not yours. From the kitten's point of view it helps them not to become over-bonded to you, so that when they go to their new home it is not so traumatic for them and they will attach easily to their new owner.
Whatever you do, make sure that if you have more than one cat it is easy to keep the kittens away from the other cat(s). Most adults do not like kittens, and an upset adult can end up spraying around the house if it feels its territory is being invaded, or if it feels stressed. Breeders' houses are sometimes a bit whiffy: this is not because the breeder is a slob, it's because breeding girls and other adults are a far more volatile community than a bunch of happy neuters, and inevitably some spraying (even if it's only from a queen on heat) is the result of the tensions that are natural in this situation.
Multiple queens or other cats in the house: let your queen decide if she wants another cat with her. I have been angered by the blinkered advice of some breeders who insist that a queen should never have another cat with her. This is absurd. One lady lost a litter of kittens because the queen was so distressed at being separated from her partner (at the insistence of the stud owner) that she suppressed ehr labour, and had to have a c-section to deliver the 7 dead kittens. This was a tragedy that should never have happened. Never separate cats who are very attached to each other just because one is going to kitten. This will cause extraordinary distress, and letting them be together will ensure a contented and relaxed queen both during birthing and after. Don't force them to be together though: the cats will decide.
If you want to have two queens pregnant together make sure that the births will not be more than a week apart, or else will be at least 6 weeks apart. Queens will often want to move their kittens in together, and this can cause problems with larger kittens stealing the milk from the smaller ones (not such a problem if the older ones are weaning). If they are more than a week apart you may have to establish two kitten rooms, and keep the queens apart, which could be distressing for them if they are very attached to each other - as with any multiple cat situation, do what distresses the cats least, not what is most convenient for you! They know what is best for them (usually). Kittens can be put together once they are weaned, and vaccinating at different times should be fine: vaccination is not supposed to make a cat shed virus, particularly if you use a killed vaccine, but it's very important that a younger litter is not able to lick the vaccination site of a recently vaccinated kitten, as this could cause problems. You may need to keep the litters apart for 24 hours, but by vaccination age this is not a problem.
NEVER allow your kittens to climb curtains. It may be amusing for you, but it will drive the new owners insane. Curtain-climbing is learned at an early age. If your kittens never see a curtain it is unlikely they will develop this habit once they leave home. Blinds work very well for me in my kitten room!
Likewise, if your kittens are brought up with scratching posts, they are far more likely to exercise their claws on this than on the new owner's furniture
NEVER carry a kitten around constantly, or allow your family to do so. This creates an obsessive dependency which is a nightmare in later life. I have dealt with a number of rescues which were caused solely by the foolishness of a breeder allowing a kitten to over-attach. One breeder even made a sling so that she could carry the kitten around with her all day. Obsessive dependency can cause an adult cat to attack other animals, children and even the spouse of the person it attaches to. It yowls and fusses for attention and to be held constantly, scratching at doors and carpets, and may develop other behavioural/anxiety problems like destructiveness, hair-pulling, inappropriate defecation etc. I have had to rehome a number of cats because they were driving their owners insane, and it has taken months of 'super-nanny' type rehabilitation to get the cat to a point where the owners can live a normal life. Please don't do this.