Benjamin Hobson's reply:
You do not mention your skill level or confidence with graphic design. I would assume from your training and exposure you are visually minded and can solve client’s problems on paper and manage the expectations and deadlines…. Thats half the battle won already.
I believe one of the key skills to being a successful graphic designer or even an agency is the [technical] ability to socialise and share the work. The presentation of the work is as important as the work itself. As such I would recommend a small course in HTML or simply learning lots about image compression and file formats. It is quite technical but is a ‘learn once’ type skill and will give you an edge when dealing with the ‘standard’ requests of having a version of a creative for a website, or an email or for a powerpoint.
So what courses should you look into? I personally prefer the self taught route, it fits around you. To this end the web is a great place for tutorials and sample code. If you prefer a more structured method then try http://www.lynda.com/ or look for/ ask around your friends to see what they can show you. A personal tutor for this kind of thing is invaluable as some concepts can require explaining in many ways before they sink in.
If you simply want to improve your skills as a designer I would learn and develop your font collection and get lots of exposure to good design. For example, subscribe to/ follow one of the gazillions of inspirational sources, the creative review blog is an obvious start. I like generic visual inspiration and look to http://ffffound.com/ but a quick search for ‘graphic inspiration’ presents a wonderful selection of sites.
My words of wisdom? Spend more time defining the problem the client wants to solve rather than simply making what they have asked for.
If you want more specific examples feel free to post another question.