One director jokingly told his actors, "Speak your lines loudly and clearly, and don't bump into any of the furniture." It's still good advice. Demetrius is not so much a character as he is a "type." He's a passionate young lover; it doesn't matter much who he's in love with. He's a good fighter, and it doesn't matter if his fight doesn't make sense. Therefore, you need to play in the moment. playing each emotion to the fullest. The best way to do this is to become thoroughly familiar with the language. You need to understand each and every word you are saying.
There really isn't a whole lot to Demetrius - think about a young noble with too much time on his hands. He has a huge crush on Hermia while he tries to avoid Helena. Until, of course, Puck helps to change his mind and he loves Helena. We really aren't given much about the four lovers in terms of characterization, other than knowing that they are young and in love. Play it like a normal high schooler that thinks he's found the love of his life!
I would suggest that you read all about the play in the links listed below because you really need to know what the play is about in order to understand the character of Demetrius. The links will give you a basic understanding of the events and characters in the play. If you have further questions after going to the links, please don't hesitate to email them. Good luck with your play!