Online dating sounds like an obvious choice for a situation such as this. Plenty of Fish dot com is a free dating site... being free, it may be that you get what you pay for though.
I'm not sure if you've heard of it but there is a good site called Meet Up dot com. It's not a dating site but it is a site which lists and hosts different groups online for activities that you are interested in doing. It's a good way to meet people...even new girl friends to go out with. This would be my first choice if I was in your situation. There are different groups on all different topics/interests...even groups for single moms. The people belonging to the groups arrange events, including activities to do together. Anything from scrabble to a cruise. The site is free to join and participate in.
If online is not an option to you, then you simply need to get out more with and without your kids. I would suggest participating more at your children's school to meet other parents there, going to places like museums, parks, science centers etc. with the kids, checking out free/local community events such as festivals, open houses and outdoor concerts etc. I know you're busy but if this is important to you then you will simply have to find the time. Depending on your social network, it may also not be such a bad idea to let your family and friends know that you're looking. Blind dates really aren't so bad!