If you Google "R d-prime" or anything like that, there are tons of examples.

I love using RStudio and the ton of packages available. But surely you can imagine the difficulties of being a graduate student with no programming background. I Google so many different package manuals and use the examples on the pdfs. However, that becomes a challenge within itself. I have read the little book of r which is a quality basic tutorial but finding open source coding in journal articles and explicit walkthroughs is what keeps me from excelling.

I recall when I learned this I found an Excel tutorial and translated the code into R. In any case, I think having to figure it out is preferable to getting ready-to-run code from somebody, because in the latter case there's a big risk of introducing errors if you try to modify it yourself without really understanding how it works; I have pretty much stopped giving out ready-to-run code examples for this reason. I think it's fairly easy to figure out, especially as the d-prime calculation is mostly basic arithmetic; there are also many R-specific walkthroughous available (for instance, this was the very first result in my Excel search: http://www.pallier.org/ressources/aprime/aprime; this is for A' rather than D', but the procedure is similar)

I guess a better question would be how do I get better at understanding how to code algorithms and mathematics if I do not have a heavy mathematics foundation?

Signal detection doesn't require a heavy math foundation, calculating things like D-prime and sensitivity are just basic arithmetic. If you find an online tutorial and/or Excel sheet and walk through the calculations, it should be pretty straightforward to learn.

Online tutorials will be a really great way to learn that sort of thing - it is never too late to learn it! The mathematics background is not crucial, and because of the variety of online tutorials, you can crosscheck the results for a sanity check while you are learning.