JUST GO! I did my first solo trip when I was 18, for a few months. Without going in to detail it really wasn't a vacation or even backpacking, was definitely dangerous and probably a bad idea. In no way am I recommending broke travel benders for teenagers. BUT, in my case specifically, it was the best thing I ever did. I got to learn that I was resourceful and street smart and could take decent care of myself even if not everyone is nice and sometimes things may get sketchy or stressful. That was 10 years ago and I've been traveling (and sometimes immigrating!) alone ever since. Just got back from kind of a tough (but good) trip in the Middle East. Mostly, to feel comfortable I try to do things to prevent issues I've had in the past. I try to blend in, I keep multiple cards and always make sure I have enough money to hop in a cab, go to the airport and go home right away if things turn sour. I make photocopies of important documents and information like phone numbers I might need or directions to where I'm staying. I talk to other women from the region and ask how they stay safe. I ignore street/ sexual harassment unless I feel really confident and if I'm in a place where it's really aggressive I plan how I can respond in a firm but polite way before I go out. Sometimes I also get a local prepaid sim card so I can use the internet and my phone when I go out. it also helps with the loneliness; I can go walk around and explore but call friends from back home if I want. Also, it allows me to use a translator.
On less of a safety note, well, I usually do okay meeting locals. A lot of people are really curious to meet foreigners. I don't advertise smoking but if you do smoke it's a GREAT way to meet people. Just ask them for a lighter! If you don't, you can always play the dumb lost foreigner card. Where is the grocery store? What does this mean? Anything. As long as you're safe about it, and depending where you are, there's nothing wrong with going up to people (preferably your age) and just saying- hi, I'm foreign, what is there to do around here? Bars and cafes are really convenient places to strike up a conversation. I also try to travel to places where I already 'know' someone- even if it's the brother of a friend or some other distant relation that comes through people I trust. Other than that, I just try to stay busy, and to stay somewhere close enough to a downtown area that I don't become isolated. Also I bring books or download games to stay entertained during the inevitable wait times.
Sometimes things do go wrong and even little things can be immensely stressful in a foreign country, especially if I'm alone and no one speaks English. I just try to accept beforehand that, hey, these things happen. I'm becoming a more savvy traveler. I'm learning how the system works here.
One kind of weird thing I like to do is get hair cuts. I don't know, it's just fun. Really lets me nail those communication issues in a relatively safe environment. The stylists always seem to have a lot of fun with me; I guess they're amused that someone who doesn't speak the language would take such a risk lol.