Put the newcomer in a quiet and secluded room. Give the new kitty plenty of food and water, a litter box, and a cardboard box or something that it can hide in if it feels threatened. Take an old blanket, towel or rags and give them to new kitty to sleep on. To encourage kitty to sleep there, lightly spray or dust the bedding with catnip. Once kitty has slept on the bedding for a few days, take the soiled bedding out, and before you wash it, give it to your resident cat to investigate. Take resident kitty's bedding and give it to new kitty (this way they can get used to each others smells)
Feed the cats close, between a closed door at the same time, so they can smell each other from under the crack in the door. Also, take an old sweatshirt that you don't care much about, put it on right next to your skin and do a workout like none before, until you have saturated this with your sweat, give this shirt to the new kitty.
If new kitty is anxious, turn off the harsh lights in the room and resort to night lights instead. Play classical music for the new kitty, it calms them immmensely. Set aside a time where you do interactive play with the new kitty so it can get used to you as well.
When you do finally put the two together, be sure you put resident kitty's food bowl down before the other, pet the resident kitty before you do the new one, to keep the alpha kitty in balance and cut down any spats that might occur. Clip both kittie's claws so if they do fight, they won't inflict that much damage. Good luck!