The hows basically involve your computer (with Office 2007 installed) creating a "digital signature" that is pretty much a security certificate that you can send to a recipient in order to decrypt the encrypted mail that's sent. A few flaws in it that keep it out of regular use for me is that the signature is not easily portable (outside of sending to recipients), it's not exactly cross-platform, and if your recipient doesn't have your signature attached to the encrypted e-mail, then they can't open it. None of these are a big deal, and inside of an Exchange system (which isn't the case of the OP) it actually works pretty nicely for internal traffic security. However, it requires a slight change to how someone uses Outlook, and that tends to be a stumbling block for it becoming widely used.
As for how well it works between different e-mail clients, I'd have to test it since I've never had to run into it personally. For anyone interested in learning how to set up e-mail encryption on their Office 2007 install,
here are some basic directions.
The problem with encryption of e-mail is that while many of the options out there are similar, there's not one that has made its way to being acceptable by most platforms and vendors, and even then it'll be a matter of time as the older generation software phases out of use before it becomes the norm. Also, naturally, the issue of key management comes into play as well, but perhaps this is something where cloud computing may very well be to the benefit of getting popular and simple acceptance to e-mail encryption-- have an e-mail "profile" saved on the cloud with settings, preferences, and saved keys, and sync them up with your e-mail client of choice when you install or reinstall the client software.