Doing plot with this data
In general, survival analysis can be said to be composed of two steps; Cox regression, with which you calculate the "hazard ratio" based on your variables, and a "Kaplan-Meier (KM) estimate", which is used to visuazlize the data.

Here is a nice tutorial for doing survival analysis with the survival and survminer packages. The latter includes ggplot2 kind visualization of the KM curves.

For the Cox regression, you can use continuous(*) or discrete variables, in your case these would be the normalized expression value of your gene and categories of your gene respectively. You can categorize the expression level of a gene as low vs high, or low vs medium vs high, based on different quantiles.  Another approach to categorize your expression data would be to find an "optimal" cut point with maximally selected rank statistics; from the link: 


  This is an outcome-oriented methods providing a value of a cutpoint
  that correspond to the most significant relation with outcome (here,
  survival)


Basically you search for the cut-point where your data is split into two such that the two resulting parts of the data show the most separation/difference in terms of survival.

* Can a Cox Proportional-Hazards Model be built only with continuous predictors?