Adding a member to your family in the form of a new cat can be fun and rewarding for everyone. Except, that is, the resident cat you already have. While most cats get along, at least eventually, you can create positive associations with the new cat during the introduction process that can make the new family member a welcome addition.

How to prepare for a new cat
It can be hard to know what to expect when introducing a new cat to your resident cat for the first time. The British Columbia Society for the Prevention of Cruelty to Animals (BCSPCA) says it's never a good idea to just throw the existing cat in a room with a new cat all at once. It's much better to orchestrate a gradual introduction process.
Before you take your new cat home, set aside a room for it away from the resident cat's favorite sleeping or hang-out areas. Add all the basic cat accessories: a bed, litter box, scratching post, and water and food. Also include some hiding places. Options include a large box or tunnel, or a carrier crate or kennel that they can hide in. BS SPCA says it can help to introduce some calming feline pheromones in the form of a diffuser such as the Feliway brand (which is available through a veterinarian's office).

Bring your new cat home
You can also use a pheromone diffuser in your home in areas where your existing cat hangs out, so that they can be surrounded by a safe, calming scent before the new cat comes home for the first time. Provide hiding spaces for your existing cat, and keep them on hand as they will come in handy when doing the "face-to-face" introduction for the first time. The Best Friends Animal Society suggests taking your new cat to their space first thing, and spending a minimum of one hour in the room with them and then leave them alone.
The veterinary blog Paws, Whiskers & Claws says the introduction process is not likely to go well if the two cats are forced to be held face to face with each other, or if the existing cat can circle the other in the carrier like prey. Also, it is not recommended to just open the carrier with the new cat and let them go.

Swap cat scents
Once the new cat has been in the room for a day or two, introduce the two cats to each other by "swapping "scents. Take the cat bed or blanket from your current cat and place it in the room with the new cat, and vice versa. BC SPCA suggests also swapping the cats' food bowls, so they can begin to develop positive associations of eating with the other cat's scent.
Notice their behavior when you do the scent swap. If your resident cat starts to hiss, spit, or avoid the towel or the food bowl, move it farther away. Each day move it a little closer to their spot. Once the two cats are comfortable and familiar with each others' scents, you can proceed to a visual introduction. It's also not unusual for the initial contact to involve sniffing and possibly some hissing underneath the door. They will likely eventually mellow out, but the time it takes for this to happen is different for each cat.

The visual introduction process
Paws, Whiskers & Claws says double-stacked baby gates are commonly used to allow cats to see each other without being able to get close to each other. If you only have one baby gate, a sheet draped down from the top can obstruct the door frame so one can't get over the top. Now you can provide meals on either side of the baby gate so that they are in close proximity and can get used to each other.
Hill's Pet says many of the same tactics of creating positive associations through the introduction process are the same whether you are introducing two adult cats or an adult cat and kitten. A kitten will be a lot more rambunctious than an adult cat, so in this case, having hiding places for the adult cat will be even more important.

Conclusion
It's never a good idea to just bring a new cat home to meet your resident cat by just throwing them together for the first time. Experts agree that slow, intentional introductions work best. Start by bringing the new cat home and slowly introducing the new cat's scent to your current cat and vice versa by swapping blankets and food bowls. Separating them with a visual barrier such as a baby gate is a way to let them get used to each other before meeting "face to face" for the first time. Providing hiding places lets each cat distance themselves when they need to.
- The British Columbia Society for the Prevention of Cruelty to Animals: How Do I Introduce My New Cat To My Old Cat?
- Paws, Whiskers & Claws: How to Introduce Cats to Each Other
- The Best Friends Animal Society: Introducing a New Cat
- Hill's Pet: Steps to Successfully Introduce a New Kitten to Your Cat