It's not just the accent that's different, since it's a dialect, you'll notice changes in the grammar and vocabulary, as well. It really depends on the region, the person, and the context, but it can be quite strong at times, for example, old women from the countryside will be very hard to understand without knowing it well.
Some common examples are ない endings changing to へん/ひん, や/やった/やろう being used instead of だ/だった/だろう, and やん(か) being used instead of じゃない(か). An example of a difference in vocabulary is なおす being used instead of もどす or ほかす being used instead of すてる.
There's a lot more details on this website
http://web.mit.edu/kansai/ if you're interested in learning more, and there are plenty of videos and sound samples to get a taste of what it's like.
However, since everybody in Japan can speak hyoujun-go, and are likely to do so with people they have just met, I doubt you will need much more than phrases like おおきに and まいど, which you should find on the website as well.