I’m about to get a kitten soon, and although I have had cats before, they have always been strictly indoor apartment dwellers. But now I have a house with an outdoor patio which I leave open so my dog can hang out there.
How would I go about making my cat outdoor compatible so that it only wanders around near my house instead of becoming a runaway feral creature? I’ve had a cat run away on me before and it never came back; I don’t want that to happen again.
Have the cat neutered.
Get a female cat. Female cats tend to stick around a given “home” spot. Toms tend to want to claim large amounts of territory, which means they have to go out and patrol it periodically, pee on things, and drive off rival toms.
Is there a reason why you have to leave the door open? Is it possible to just put the dog out and then keep the door shut? Maybe adding a screen door, so at least you can still see the dog?
You might be able to train the cat to mostly hang out in your yard (I did it by spending many, many hours outside with them with a spray bottle, and every time they approached the perimeter, I squirted them to retreat into the center of the yard) but there’s going to come a time when he wanders off. How about harness-training him? You need to get a harness specifically for cats and then start out with putting it on him, attached to a leash, a minute at a time. NEVER use a collar to leash a cat unless you want a dead one. Although, a cat can get out of any harness made if it really wants to. They find a way.
My former housemate “patio trained” his cat. Plese note though, the cat was always either supervised or within sight at all times.
The first few times the cat ventured out and tried to step off the pavement, he got scooped up with a “No! Stay on the patio” and plopped back down on the pavement stones. This happened again and again. Cat figured it out – this was also a well-behaved little guy, who would obey the rules – and always stayed on the stones, never leaving the patio.
When we shared a house, FatCat (a strictly indoors critter) was also allowed out (supervised by a human) and he decided to “do what OtherCat does” and he also stuck to the porch. FatCat is a little rebellious though, so a human had to be lingering nearby in case he decided to be naughty and wander. The well-behaved cat would stay put although we always kept a watchful eye through the patio doors and that cat was never truly left unsupervised.
Someone I know has a dog and cats and installed a dog door on the back door. The door has a magnetic close on it, and the thing that releases it is on the dog’s collar, so that if she wants to go out, all she has to do is walk up to the door (I think she has to be at the door, not just near it) and go out, while the cats can’t get outside at all. It’s a pretty nifty thing.
I should add that I was always outdoors with my cats when they were off the harness. I’d never have left them out there unsupervised. I think that’s part of the reason they stayed in the yard - because I was out there. If I hadn’t been, they probably would have ventured off at some point.
Keeping a new cat in the house for several weeks, then gradually introducing it to the yard, helps. Cats are territorial and will stick around their nest. Neutering the cat contents it with a smaller territory as well.
My female cat has been indoors her whole life. Once I left the door open and she wandered outside. She looked at the sunlight and examined her surroundings for a minute or so.
Then she went back in. Presumably if a cat gets used to a certain territory, it will want to stay there.
I’d keep it inside for a while. We have a female cat (the previous two wandered away). We kept her in for a few months until she was used to the place. Now she’ll go around the back yard, and the front, and sometimes as far as across the street if we’re nearby, but that’s it.
Now that I think about it, the first cat was found in a box by someone at my moms office - she disappeared within a month. The second was found in a similar manner I believe, but was more of an outdoor cat. He disappeared overnight a few times before he finally left IIRC.
Like BobT sez - if your cat is quite used to where it is, it’ll hang around - keeping it there in the beginning is the hard part. 
We had two cats who were strictly indoor cats. Neutered and declawed females. Once we put them outside, just to see what they would do. All they did was sit at the door and cry to be let in. They loved to sit in the back window and watch the dog outside, but they had no desire to go out.
Shoshana’s advice is most consistent with my experience and reading about cats, and I’ve had one or two cats as a member of my household for my entire life.
Neuter your pet: The most humane thing you can do, regardless. And the bit about smaller territory applies to both neutered male and females. Neuter your pet early at 5 or 6 months, before he or she gets into a spraying habit.
Gradual access: Supervise your cat outside at first, and the first few times, limit the outing to just a couple minutes. Establish a boundary ahead of time, and don’t let your pet cross it. Start with just a patio or small patch of lawn. Expand this territory gradually. Don’t let the pet wander out of sight of your door until he/she learns the lay of the yard and knows which entrance belongs to you. Keep your pet between you and the door, so in case it begins to exceed your preset boundary, you can scare it back inside
In fact, I began to startle my cats the first time in a new yard to try and see what they would do. If they don’t run for the door they came out of, then it’s not time to expand their “run.”
Eventually your cat will be able to go outside unsupervised. It will establish a “beat,” to patrol the boundaries of it’s territory. It may still get into fights or standoffs in order to defend its borders. This is normal, healthy cat behavior.
But, you expose your cat to additional risks. Fleas and other parasites - so use Advantage flea control treatments monthly. Keep the vaccinations up to date. Annual checkups. Examine the cat regularly for scrapes and bruises, especially after fights.
If you live in an area with coyotes or other hunting animals, make sure your cat has a safe place it can retreat to, either a tree or a small outbuilding or somehting similar.
Feed your cat on a regular schedule. Do not leave food outdoors for your pet. Require it to come indoors to be fed.
Make sure your pet wears a collar with an ID tag, including your phone number.
If you can, teach your pet to respect motor vehicles. Scare it with your car in the driveway. Too many cats do not have the proper fear of cars.