I would recommend you to read some of the post/blog about

1. Career prospects in Bioinformatics and Computational Biology
2. Top reasons to do PhD and Post Doc in Comp. Bio
3. How Did You Learn Good Practice In Bioinformatics/Computational Biology?

Courses that to build concepts in the area of Bioinformatics and Computational Biology (I would highly recommend)

1. JHU Data Science Course
2. UCSD Bioinformatics/Comp Bio Course
3. Mount Sinai Systems biology Course
4. Linear Algebra is the most basic thing that is high required if you want to pursue your research/studies in Machine Learning and for NGS data analysis
5. Machine Learning
6. Data Analysis for Genomics: particularly for NGS data analysis

In terms of programming: (in no particular order)

1. Unix/Linux programming
2. R programming
3. Perl/Python programming
4. C programming

There are a lot of good answers already written in this thread. I would like to give my own views through the links I will post below. These are my personal opinions in being in the field and also from other people and I have been writing for a while in Quora. Biostars will provide you a lot of threads about the field and what learnings one should take and how to evolve the knowledge base over the years and also keep abreast with the technological innovations in the field. This forum is an excellent place to be. I am just putting my thoughts from Quora. Feel free to read them and ask questions if you have any doubts. Below are the links

1. What is it like to major in computational biology?
2. What is it like being in bioinformatics?
3. Can one switch to a career in Bioinformatics with pharmacy background without formal training in computer science, advanced maths or statistics?
4. What's the best major for someone who wants to go into bioinformatics?
5. Are there any lucrative career paths related to bioinformatics?

Now from some internaltional blogs from market analysts about the growth of the field by 2020 due to upsurge of data in healthcare and genomics.

Global market of Bioinformatics by 2020

Bioinformatics Market outlook by 2020

Things to learn,

1. Unix/Linux programming
2. Any scripting language (shell/bash, python)
3. Statistical Programming with R/Matlab/ SAS
4. Data Structures and Algorithms
5. C/C++ or Java Programming
6. Molecular Biology with interest on genomics and proteomics for NGS field
7. Machine Learning, linear algebra, Statistics(both basic and advanced).

Someone can add more. These are my thoughts but there is no dearth of learning.

Coursera provides pretty comprehensive courses that one can look out for.

Another thing will be to get training in some labs to have hands on with your masters thesis and get the feel of the field. Good luck!

I would also recommend the following book

Vince Buffalo, Bioinformatics Data Skills: Reproducible and Robust Research with Open Source Tools

it gives a very practical view, what kind of world you are getting into and how to overcome its obstacles .