I recently found some work through one of the freelance websites but had to back out. I'm a full time software engineer but I am also a full time dad and husband, and between shopping, cooking (I work from home so these tasks tend to fall to me), going to dance and music recitals etc., it was just too much.
Regarding networking, if your employer sends you to technical conferences, it's a great way to practice. Quite often I strike up a conversation over the breakfast buffet. People are usually quite relaxed and willing to chat while sugaring their coffee and grabbing a pastry. Everyone is in the same boat as yourself; they all want to network, build up useful contacts and potential business partners etc., so they will eagerly tell you about themselves, exchange cards etc. After you have been doing it for a while, networking can become natural and fun, and it's very worthwhile to cultivate a friendly and outgoing manner. You never know but it may result in your next job offer. Good luck!