Usually people don't actively search for relationships. It's kind of like this, actually. If you feed the other parts of your life, they all improve the relationship aspect. If you improve your health, it does great things for your social life. If you diversify your hobbies it makes you a more interesting person. Also good for your social life. If you focus on education or work more seriously, it also helps.
Really anything that helps a person grow as one and not be a bland character is good for your social persona. Actively seeking people isn't what one should do, rather a side effect.
Example: You like tabletop games. You want to play tabletop games with real people. You search for clubs like that in your general area. If there is one, you go check it out. You then proceed to go a few more times (become a regular), and boom you know people because you played games with them.
Now you might say to me, but Apiks, what if there aren't any of the things I like in my area. Well that definitely sucks and in most cases isn't good at all. What one does is that they either create it themselves, find something different or just procrastinate at home because, let's be honest, you don't like going out of your home. (also known as comfort zone)
Since the first one we'll assume isn't viable and the last one is the thing we're trying to avoid, the best next thing to do is to go to events, really. You see a convention you can be interested in a few cities away? Go there then and enjoy, even if it's just looking. Most of the time they have even more stuff always going on than the theme. Extra points if you participate. This is the single most useful thing I use Facebook for.
Example: Anime conventions feature not only anime but cosplay, gaming, japanese culture and some things that have nothing to do with anime.
If you happen to be a person who's good off financially, then that can help you immensely in regards to participating in things, confidence and being able to afford to experiment. It sucks, I know.