Introductions can be hard. Like one of the other posters said, you need to give them time. Remember that cats are very territorial, and this to them means they have to redivide the territory, and nobody likes handing over territory, including your cats who were there first.
I made the mistake of putting my second cat directly in with my first one, and I had an open war on my hands for a month. They do get along now.
The best way indeed to introduce them is put the newcomer in a seperate room. There are several good reasons for this:
a) if the newcomer has parasites, isolation is always a good thing, this way you can find out about them before your other kitties are infected.
b) This way the newcomer has the time to really get used to the new environment and investigate once space at a time and get comfy, and also, get used to you.
c) Your own cats dont lose that much territory at first, and they get to sniff out the newcomer through the door without the situation escalating.
Also, wash your hands when you have petted the newcomer. The other cats might get 'jealous' if they sniff the smell of their new rival on your hands. Dont forget to give your old cats plenty of attention and play with them to alleviate the stress of having a new cat in the house. Same for the newcomer, if you can, and he does trust you enough, try to play with him, so that he too can get rid of his stress.
It is definitely common for them to take a while to warm up to each other. You can also try to exchange scents and let them investigate each others rooms before letting them actually meet. Try rubbing a sock on each cat and exchange the scents that way. Then put the newcomer in the other rooms, so he can investigate the rest of the house quietly and get used to the smells there, same for your other cats, let them investigate the room your newcomer has been in.
After a couple of days, to a week, depending on how upset both sides are, you can let them meet, just briefly, and built up in time. Never leave them alone, before you re sure they get along, always be there to supervise.
As long as no blood gets spilled, everything will be just fine. Just respect the pace of the cats, and start over if you notice that you went too fast.