I had to handle the introduction of a small cat to a big dog. Now I am introducing that cat, that is grown-up, to a puppy.
The trick, from what I got, is slow and controlled introductions.
Always aware of potential problems and with ways to minimize them.
For initial face-to-face introductions, in both cases, I have only held the cat. However, I know of people that use a leash and harness for cat control and a leash and head halter for dog control.
In the first case, after maybe around 2 weeks (maybe 3), with those gentle introductions, they were both playing along. They ended up being good friends and even sleeping next to each other various times.
On this new case, I am on day 3. The puppy is not that aware of the problem that could result from leaving the cat alone with him. The cat, when is next to the dog, is most of the time in predatory mode. But as I am holding the cat when those interactions are happening, I always rub the cat under his chin and he gets more relaxed. However, one can see the cat's ears always looking for any sound that may potentially put him in danger.
Update (4 weeks later)
We haven't forced interactions.
Dog and cat already share spaces, however the cat is not yet 100% relaxed with the dog's presence all the time.
They walk next to each other and they sleep when one of them are in the same room.
Update (almost 1 year later)
They are great friends now. They have been like this for a while, but just reminded myself to update this now.
Update (2 years later)
Still good friends. Each have their own boundaries and make sure the other one knows about it when the other tries to cross, or crosses it: the dog is more food related, the cat I would say is more about pickiness.