Do you have a crate for him? Do you know about crate training? It's the best, fastest and most humane way to potty train an animal. There is LOTS of information about crate training on the web if you want to google it.
Just remember, you have a dog. He might be a chihuahua, which means he's tiny, and it's very, very easy to become over-protective and treat him like a precious, fragile baby, but he's a dog first, and any rules that apply to dogs apply to him.
As you live in an apartment and can't know what other dogs have been around spreading what kind of diseases, I personally wouldn't take him outside till he's fully vaccinated unless there's a spot you know is safe. If your apartment has a patio of any kind, you could take him to that, even put a pee pad down if you wanted to, so he starts getting the idea that outside is the place to eliminate, assuming that you want him to be an outside potty dog. Some folks here (me included) have their dogs trained to pee pads. Tango and Jazz don't go outside to potty. They WILL potty outside when I'm out in the garden with them, or on walks or whatever, they're just trained to eliminate in designated areas when they're inside.
What are you feeding him? Get the highest quality food you can possibly afford. You will extend his life and make it a much healthier one with extremely good food. Go here: dogfoodanalysis.com. The premium foods are more expensive, and some aren't sold in a chain type pet store like PetsMart, you have to go to an independent store to buy them, or buy them online. But the good thing is that these little guys are so small, it takes them a long time to get through even the smallest bag, so you don't have to spend a lot of money very often.
Have you gotten him to the Vet yet? A thorough vet check is advised, and preferably a vet who has some experience with small breeds.....if you plan to get him neutered (please do!) that experience will come in handy, and lessen your concerns when he goes in for surgery.
We love pictures here, so any pix you have of the little guy we'd love to see 'em.
Good luck with your new baby, and keep us informed, and ask as many questions as you want to, the more the better.