I've always done them by myself, and I have an anxiety disorder. It helps to pack a little bag for social emergencies - some cool comics, some candy, a drink. So if you feel depressed or worried, you can 'retreat' for a moment and regather.
Treat every couple of hours like a little adventure, and go out. A really good way to find people to chat to is to spot something cool - someone's hair, clothing, attitude, voice, art. Compliment them (sincerely) and ask how they're going at the con and what they've had fun doing. Even if nothing else has happened, you've had a positive interaction.
For lunches, ask if you can join a group and note you're there alone. Every group I ever talked to invited me in to chat. Always offer to help tip (if you're in the US). If someone's stuck on a desk and you've been talking, offer to grab them a coffee or soda.
I remind myself that my anxiety means I tend to misjudge people's reactions, if I think I've screwed up, and probably no one has noticed at all.