With regard to your depression, I agree with Zeph and Sirius that professional therapy is likely the best option.
As far as your social problems go, there are numerous ways to approach this. Several have already been discussed by the others, such as joining a club or organization, learning social cues through exposure, etc. Being able to smile, make eye contact, and ask/answer questions are basically your entry fees for just about any form of socialization. It's really the only way to get to know people. However, I've never really believed in "faking" when it comes to social situations. There's being polite and sociable, which is fine. But then, there's pretending you're something you're not. That's a line you should never cross, in my opinion. I'll try to explain it using a metaphor:
Everyone has different "hats" they put on, depending on who they're with and what situation they find themselves in. You have a hat you wear when around your family, and a different hat you wear around your friends. Then you have yet another hat you'll wear in class with your instructors and fellow students, and still a different hat you'll wear at work, if you have a job. These hats represent different ways you behave. Everyone does it. You're going to act differently around your close friends than you do around your family or coworkers. It's fine. All it is is different levels of openness. It's ok to wear different hats.
However, never should you put on a mask. This would mean pretending to be somebody you're not in order to please or impress other people. It's lying, and it's detrimental both to your own self esteem, and to those you're lying to (because they're getting something that isn't real or true). It's important to be able to express yourself honestly.
When you express who you are to people, you're essentially putting yourself on the table for examination. In my opinion, it is impossible to make others like you. That decision is entirely in their hands. You can be as nice as you want to some people, and they'll still hate you for some reason or another. However, if you show people who you are by expressing yourself in an honest and civil way, you allow them to make a more informed decision as to whether or not they want to engage in any sort of socialization with you, be it short-term or long-term. This increases your chances of meeting people with whom you'll really get along. Those people will be drawn to you when they see who you really are.
As for specific ways to express yourself, here are a few that I use:
— Dress how you want. Don't feel pressured by social/societal expectations of how you should or should not dress. Wear what you like, and what you're comfortable in.
— Tell stories. It seems like my conversations with friends—or acquaintances with whom I feel compatible—inevitably devolve into me telling some crazy story about something dumb/tragic (but funny looking back on it)/unusual that I've experienced. Everyone has experiences worth talking about, whether you believe it or not. Even the most mundane things can seem interesting if told in an interesting/compelling/entertaining/funny way. Telling people stories about yourself also gives people a glimpse into how you think/operate/respond to things. And if somebody else tells you something interesting and it reminds you of something interesting you'd like to tell them, don't be afraid to do so!
— Tell people what you like, especially if they ask. Don't be afraid to talk about your hobbies or interests, no matter how obscure they may seem. You might find people who are into the same thing. And if somebody doesn't know what you're talking about, explain it to them. They might just find it really interesting! Two important things, though:
- People will have different interests than you. You must understand and accept this. It's perfectly ok. Just try to avoid criticizing or bashing their interests. For example, if somebody tells you how much they love dubstep, and you absolutely hate it, simply say you've never really been able to get into it, and explain—politely but truthfully—why. At the very least, it will give you practice in effectively articulating your thoughts and opinions—a VERY important skill to have.
- When people have different interests than you, don't simply go along with what they like because it will please them. Once again, this is lying. This is putting on a mask. And it will really come to bite you in the tail when they start talking about it enthusiastically and asking you what you like about their interests. For example: I ran into a fur online who asked me what I'm into. I mentioned knives, and he said that he loves and collects them, too. I started asking him about his collection and talking about mine, throwing around terms like "full tang," "drop point," and "assisted folder" around—terms that any knife enthusiast would likely be familiar with. He wasn't able to fake it for long, and was quickly forced to reveal that he'd never even held a knife before.
All this is going to take time. You certainly won't be a social butterfly overnight. I'm still socially awkward in many situations. Many people are. The key is to seize every opportunity to learn, to practice, and to experience. With time, things will indeed get better.