Generally, relationships form between people that spend time together. Often, this is in a circumstance where finding a partner isn't the primary objective (school, college, workplace).
I, myself, met my girlfriend in highschool.. And we've been together for over 10 years now!
How do I meet someone?
If you're concerned about the likelihood of meeting the perfect partner, I'd suggest treating the situation like a math problem.
Statistically, you are more likely to encounter and bond with another person if you're:
a) Frequently meeting people and making friends
b) Seeing those friends on more than one occasion.
How you engineer these situations is the challenge. For example, perhaps you might meet someone at a party who you enjoy spending time with.
In order to get to known them better and form a stronger bond, you'll need to find an excuse for repeat contact: Ask them out on a date, suggest you 'hang out' some time, or even show an interest in a hobby or pastime of theirs, in the hope that they might invite you along.
Like most things in life relationships seem to work best when you act natural, don't try to hard, and go out there with confidence and good intentions. The rest should hopefully fall in place.
And if all else fails, there's always internet dating.
If that's the road you want to go down, then here's some helpful advice on the do's and don'ts of internet dating: