You've had some really good advice on here.
One other thing I would remember is that when you are talking to people, don't interrupt them and maintain eye contact with them so they feel you are really listening to them.
Start conversations with things such as
"That's a lovely dress your dd is wearing! Where did you get it?"
You can then go on about how you'd like to find some reasonably priced but good quality clothes for yours but it's so difficult etc, they then agree about kids clothes and before you know it you are empathising with each other about the state of the market for childrens clothes.
Empathy is the key. If you have a problem with one of your children, night waking or something, mention it to one of them and ask if they can suggest a way of dealing with it, mothers love dishing out advice, they love it when someone asks them for their opinion. When you see them the next week you can say "Oh I tried your suggestion! It really helped, thanks very much!" It's a sure fire way of getting people to like you!
If you look at any mum and tot group you will see another mother on her own, either she will be quiet like you, or a newbie who knows no-one. Strike up a conversation with these, they'll be eternally grateful that someone has made an effort.
As for the non-smilers, I win them over with politeness, I never stop smiling at them and I always say hello and goodbye and eventually they will return the smiles, they have to eventually!
Never tell anyone about how depressed or lonely you might be, people tend to give these kind of subjects a wide berth, they are for discussing only with people you know well. Stick to everyday situations and circumstances, be prepared to laugh at yourself, if you make a faux pass, acknowledge it and laugh at it, they'll laugh with you and it makes you seem more approachable and laid-back.
But above all, be prepared to listen - people love talking about themselves and they love a captive audience. Have a few lines prepared for when conversation runs dry, and be ready to move on so you are not just sat with the one person, you can go and play with your tot for a minute or help bring the drinks out, so you don't come across as under-confident or dependant on just one conversation.
Be yourself. I'll bet you have lots to say to people who really know you, shyness is a way of hiding yourself, so try to come out from the shyness and be proud of who you are!