What you're trying to do with the data that you have doesn't sound like the right fit for machine learning:
If I'm understanding you correctly, you have a data frame of Job Title and Company, and you want to associate each posting (row) with an Industry. This might be a reasonable supervised problem to tackle if you had industry labels, and other information about each post (e.g. salary, years experience required, basically other columns in your data frame that described the job posting); specifically you'd be looking for some sort of classification algorithm. Alternatively if you had the other data, but not the industry label, you could use unsupervised learning (some sort of clustering algorithm) to find groups in the data that might naturally separate your data by industry (e.g. if jobs in a certain industry were typically similar in terms of job title and your other data).
As it stands now, if you're really interested in understanding the industry of each job post, you'd probably be better off doing some sort of look up of the company name to get the Industry. (E.g. Wikipedia has an industry section for major companies, here's an example: https://en.wikipedia.org/wiki/Amazon_(company)).
If I were you I'd start with some introductory books to get a handle on what machine learning is, and what it can do.
From a "classic" machine learning perspective I think that "An Introduction to Statistical Learning" would be a good place to start.
"Deep Learning with R" is a good primer for getting started with deep learning (in R).
You could also consider taking an online course, I found the Andrew Ng one on Coursera to be a great start for me.