Machine learning consists of parametric optimization to reduce some error function on training data and then use the learnt parametric model on unseen/held-out data and evaluate. The first step is to construct the right parametric model by studying the data domain and then iterate till the performance is achieved within acceptable level. Machine learning research is highly mathematical, but you can start by using some open source ML tools and tweaking the models to get a feel for the capacities of different models.

Some topics you should familiarize are: Probability Theory, EVD/SVD, ANN, ML/MAP estimation, Minimum classification error training, SVM, LMS fitting, PCA/ICA, FSM and HMM.