I am a professional dog trainer. Most likely since one dog is a puppy, you will have no problem introducing them. However, it is best to introduce them in a neutral territory. It is best to introduce them in a large fenced in area and have the leashes loose on the ground. Once you pick up the leash, you are restricting the dog and its fight or flight response may come out, and the dogs would be more likely to fight. If you see any kind of aggressiveness, most likely this would only come from the adult dog, correct it with a verbal command. Never use any physical corrections, as that will encourage aggression.
In most cases, a puppy will get along with most adult dogs. Adult dogs give puppies extra leniency since they puppies, (kind of like we do for young children), however, it is around the age of 7 months or so, that adult dogs will expect puppies to act more like an adult dog. The adult dog may start “correcting” the puppy now for what the adult sees as inappropriate behavior.
You cannot decide which of the dogs is the alpha. They will decide it based on their individual temperments. In the beginning, though, the puppy, unless it has a very dominant nature and/or yours has a very submissive nature, will be below your dog. As the puppy matures it may change. You need to gain good leadership over both dogs, but also respect how they work out their hierarchy. If you favor the subordinate, that’s when you can cause a dog fight.
Verbally correct bad behavior, and give lots of high-pitched praise for good bahavior, and things will probably be fine. You also need to be a calm, consistent leader that follows through on every command you give.
In most cases, dogs are fine when you separate them unless them become extremely dependent on each other.
Good luck!