How can I tell if the mating has been successful ie that the female hamster is pregnant?
If the female doesn't come into season again 4 days later, she's regarded as being pregnant. Given that the babies only stay in her for 16 days, 10 days after the mating, she will start to become decidedly pregnant - her abdomen will swell (no, she's not getting fat), and her nipples will start to become more pronounced.
What do I do after the mating?
You return both hamsters to their respective cages. Female hamsters will need extra food during the pregnancy. High protein foods like tofu, boiled egg, wheat germ (to aid in birthing) can be added to the diet. She can still be handled but it's best to leave her alone when it's closer to the expected birth date. Clean out her cage at day 14 and take out the exercise wheel, provide her with extra nesting material (eg shredded paper). Then put her cage in a warm, quiet spot with as little disturbance as possible and wait...
Ooo - the babies are here - what now?
Let her nurse the babies till they are about 3 weeks old. DO NOT disturb the nest during this time as she may decide to turn on them and eat them. The cage will smell during this time - that's unavoidable, any attempts to change the bedding material would increase the likelihood of cannibalism so it's best to just leave it for the moment and put up with the smell. Sometimes despite all this, the female hamster will still cannibalize her young, this is common in female hamsters bred under 4 months and in older females who will cull some babies to reduce the numbers in the litter. Continue with the high protein foods (other ideas are bread soaked in milk) during this time. At about 3 1/2 weeks of age, the hamsters are ready to be sexed and weaned - they are no longer reliant on their mum for nourishment. You can keep them in 2 different boxes/cages (all the male hamsters in 1 cage and the females in another). They can be kept in these groups for a further 2-3 weeks. In the meantime, you can find new homes for them and they can go to their new owners at 5-6 weeks of age.