Who will enforce the laws, without a government? Who will enact those laws to begin with?

Polycentric law is a well-established concept, as is judicial precedent. If you think of judges as finding the law in any given case from basic principles and precedent rather than simply prosecuting people based on a set of rules handed down by someone, it makes more sense. If you're looking for more info, here's a pretty good intro: https://www.youtube.com/watch?v=8kPyrq6SEL0

If a group of people came together and draw up a code of conduct - would they not be a de facto system of governance?

Governance, in the sense of leadership / guidance, sure. One of the more common definitions of government is as "a compulsory political organization" that "maintains a monopoly of the legitimate use of force within a certain territory" (http://en.wikipedia.org/wiki/State_(polity)#Definitional_issues). It's mostly the words "compulsory" and "monopoly" that I have issues with. If you want to set up an organization with a certain code of conduct, I have no problem with that - provided that I am not forced to join. If I can create my own group, or live under no group, then I have no issue - to each his own.

Then we come to the idea of implementing those laws. If no coercion is involved, then wouldn't it not be "laws" and more like "suggestions"?

This is a common point of contention. In my view, force/coercion can be legitimately used against those who have themselves initiated force - if someone starts throwing rocks at passersby in the street, I'd say that I'd be justified using some amount of force and/or coercion to get them to stop, provided it's comparable (if he's throwing rocks and you drop a nuke on the street, you're obviously outside the bounds of comparable force). Otherwise, how do you deal with someone who's putting other people in danger? Asking them politely to stop doesn't usually work.

Of course, all of this is founded on the idea that property is a valid concept, and that voluntary association / hierarchy is fine, as long as it's actually voluntary - which probably means I'm not that likely to convince anyone in here.

My question for you is this: as an anarchist (I'm assuming that you are - correct me if I'm wrong) how would you solve disputes and/or prevent someone from just "instituting his own governance over others"?