Probably the first thing you want to know is whether you can make your Plone site look like your existing site.
The short answer is yes, but obviously you'll want to prove this to yourself.
This is where it gets complicated. Theming in Plone version 3 has been a bit of a nightmare. So theming the traditional, native Plone way can be a bit of a baptism of fire (and worse because it is the first thing you'll want to do - particularly if you need to create a proof of concept for your boss).
Theming the traditional native Plone way
You can start off by theming through the web - this means dipping into the Zope Management Interface, finding a section called portal_skins and customizing various templates and stylesheets. You can do quite a lot this way, but you'll eventually want to make your changes portable, that is turn them into a module/product you can then deploy on a production site, or on several sites.
At this point, you'll want to create your own module/product, which you can do by generating some skeleton code and then dropping your own bits and pieces into it.
In the MSD we have our own theme product, which we deploy on all our sites and then customize through the web with banners and custom stylesheets.
Most of traditional theming is covered by the Theme Reference Manual on plone.org and there are also useful tutorials on the Penn State Weblion wiki.
Rules Based theming - the "easy" way
This is the new way of theming. Still in its infancy and a complete pig to install, but once installed very straightforward to use. We haven't tried it yet in production, but others are using it with great success and we've found it very promising in experiments.
The principle is that you treat each Plone generated page as if it were simply a "feed" of data which you can then transform using a set of rules and a "static" template - which is basically an HTML representation of your site (no templating language required). The static template can be anywhere really, so, if you're demonstrating using Plone to back an existing site, you could use a page on your current site as the template and just write the rules.
Make a start by looking at the Theming manual on plone.org, which is geared towards using collective.xdv (a Plone friendly version of rules based theming).
Don't give up at the installation stage - ask for help. It is a lot less painful than traditional theming - believe me. What's nice about Rules based theming, is that it treats you like a proper web-designer, it doesn't assume that all you want to do is point and click, it gives you complete autonomy over your design, but it also means that you don't have to delve into the innards of Plone until you've got the stomach for it.
That said, you may find that somewhere down the line you'll need to tackle some of the theming concepts - if you need to adjust templates for instance to get a slightly different "feed" from your plain vanilla plone site.