If you want to start playing with some deep learning models, I would highly recommend this page. It provides some basic examples that run right in your browser. Also, this page provides a great guide to working with neural networks without getting bogged down in a bunch of mathematical equations.
Another great resource is Caffe. Caffe is a deep learning framework that will let you define a wide variety of neural networks by just writing a text file. You can run Caffe applications in CPU or GPU mode (a lot of open source deep learning code will only work with GPUs, so being able to run things either way is a nice feature).
If you want to do computer vision, make sure that you read up on fully convolutional neural networks, because they are the big thing right now.
Remember that story about a program that was able to learn how to play just about any Atari game? That is called reinforcement learning, and that's a big thing right now too. Udacity has a great course on reinforcement learning.