The best way to learn social ballroom dancing is through private dance lessons. When you come in on your own, you actually get to spend the entirety of your training dancing with a professional instructor. With a partner, there's a bit of a "blind leading the blind" aspect at times. It can be a great bonding experience with a loved one, but if you're looking for results, one-on-one time is the way to go. You don't have to worry about anyone's progress but your own!
Once you do get started with private Salsa or Swing dance lessons, the best way to practice is by going out dancing. If you don't have a go-to dance partner, you're sort of forced to meet new people and new dance partners. It's a fantastic way of connecting with other dancers and forming great friendships along the way. If things go really well, you might even meet someone you like enough to bring to your lessons down the road. ;)
Don't get me wrong, dancing with a regular partner is great. You can build a solid, comfortable connection with a friend or significant other in a super fun environment. But that doesn't mean you can't or shouldn't learn without one. Social partner dancing is for everyone, no matter your walk of life!