Deep Learning and NLP are quite complex subjects, so if you really want to understand them you'll need to follow a couple of courses in the field and read many papers. There are lots of different techniques for converting words into vector representations and it's a very active area of research. Socher's DL for NLP tutorial is a good next step if you are already well acquainted with NLP and Machine Learning (including deep learning).
With that said (and considering it's a programming forum), if you are just interested for now in using someone's else tools to quickly obtain vector representations which can be useful in some tasks, one library which you must look at is word2vec. Take a look in its website: https://code.google.com/p/word2vec/. It's a very powerful tool and for some basic stuff it could be used without much knowledge.