I have really skewed RNA-seq data, what's the best way to normalise it? Preferably in R!
Welcome to RNA-seq. This is not at all unusual, as RNA-seq raw data are not normally distributed. People typically approximate it via the Negative Binomial distribution. I suggest you check existing packages as Devon suggests in his comment for normalization and differential expression (or anything else). Typical choices are DESeq2, edgeR or limma, but there are others as well.
This guide might help you get started. Please also use google to explore existing threads both here at SE and over at biostars.org.
Most basic questions have already been discussed there and are informative to get started.