[FishNChips]

sounds like you'll be fine as other posters have said you're certainly not going to burn a bridge by staying a couple extra weeks and offering to help on the side (be careful on this one though - I don't know how much freelancing experience you have but from what little I know about it there is lots of tax stuff involved and you'll want to be sure that you have the terms covered clearly before starting to do the work).

My one suggestion though, write a letter of resignation. Short and sweet "I've enjoyed my time here, learned a lot blah blah blah. Another opportunity / more benis / better pay blah blah blah. I am giving you 4 weeks notice (or whatever it is)" Then you can walk into the boss and say "I'm here to turn in my resignation.

wait, one other tip:
if you are a valued employee they may ask "what can we do to make you stay?" This is a tough one. If you really like the place you can ask for whatever it is that you think will make you want to stay, but I think its probably better to just say "I'm sorry, but I've made my decision and I'm going to be making this change. There isn't anything that you can do." My personal opinion is that if there is more that they can do to keep you then they should have done it rather than holding out... but that's a philosophical Q for a later time. Just be aware that it may happen.

Good Luck with the change!
FishNChips