I think the most direct way to portray an accent is to reinforce it with idiosyncrasies various groups have when they talk. This was mentioned earlier regarding the way people pronounce words differently in a phonetic sense, but you can go further than that by injecting the grammar of the speakers native language into English. This action further shows how this person is a non-native English speaker, and thus speaks differently and with an accent.

Take Polish for example. The Polish language does not use articles ('a', 'an', 'the'), so you can often reflect this fact in the character's speech.

If someone asks you to turn on the the lights in Polish, they say, "włącz światła". However, this phrase literally translates to "turn on light(s)", not "turn on [i]the[/i] light(s)". Notice the lack of an article. You can use small difference in speech patterns in order to convey something as big as the characters native language, accent, etc.