How to improve internal communication and teamwork in an office environment?

Of course it would depend on the size of your office, and the type of things you are doing already, but something simple to start with is a newsletter. A newsletter can be sent through email and is fairly easy to put together. Although you will need someone to be in charge of content, layout, etc. Don't be overambitious! You may need to start with a quarterly newsletter, not a weekly one.

If you are a larger company a company intranet is also very useful (if done correctly). Sometimes it may seem hard to get employees to pay attention to these things so try incorporating things like employee spotlights/profiles, or contests, in order to get people's interest.

I also love a good team building event to get to know people. My office puts together activities all the time (lunch and learns, laser tag, cook offs, etc.)