Learn this before starting with machine learning

You are on a very good start if you learn Backpropagation and use it to play with some Neural Networks and then learn Restricted Boltzmann Machines and contrastive divergence.

The path I would recommend is:

1. Linear Regression and Gradient Descent
2. Logistic Regression
3. Neural Networks and Backpropagation
4. Autoencoders
5. Restricted Boltzmann Machines and Contrastive Divergence
6. Deep Belief Networkd
7. Convolutional Networks

And you are ready to try deep architectures.

I strongly advise you to actually code a neural network with backpropagation, a RBM with contrastive divergence and an autoencoder if it's easy to find quick applications for those to get you interested.

I don't know what kind of programming language you use but I'd recommend you to use Python,Matlab/Octave or R. If you know Python Theano will be a very good way to experiment with deep networks.