Changing to a career in software engineering?

I will be finishing my masters in applied and computational mathematics in a year or so and am considering entering into software development. I am new to this field, and have no idea how to prepare for a career in this profession. I would like to know what skills I should have (programming skills) in order to get a job as a software developer or software engineer? I know C++ and am learning Java on my own. When ever I look at job listings, I see a long list of desired skills that employers are looking for (this is for the entry level positions), is it possible to have all these skills upon graduation? Should I obtain certifications, if so, what type of certifications should I seek? I know I'm asking a lot of questions but I am really confused as to how I should begin this process. Thank you so much, any advice would be helpful.