"The man is playing in the restaurant."
Translation:Der Mann spielt in dem Restaurant.
"spielen" is incorrect because that normally goes with "you/(Sie)" or "we/(wir)". "Der Mann" can be replaced with "it/he", so the correct ending would be "spielt". The verb is normally placed second in the sentence after a noun like in english unless it is a two part verb (ex. will know).
Just to build on what qbufm07 said, English has a "continuous aspect". For the laymans reading this (like myself), "continuous aspect" just means that in English we say "The man IS PLAYING." German doesn't have a continuous aspect, so "Der mann ist spielen" doesn't work. It is simply "Der Mann spielt" (the man plays). If translating "der Mann spielt" into English, both "the man plays" and "the man is playing" are acceptable. There are exceptions to the continuous aspect in German, and I believe (if memory serves) you encounter 1 or 2 in Duo (I think "Ich bin am Lernen" was one?). Some exceptions can be found here, but given that we are learning very basic German with a free program and not taking German Studies at university, we should probably just acknowledge that they exist and move on: http://en.wikipedia.org/wiki/Continuous_and_progressive_aspects#German