You don't need R, just two lists of genes, one list for unregulated and one list for your other category. You can paste each set into BioVenn to make a roughly proportional circular Venn diagram. If you want a list of overlaps, just use grep between the two lists:

$ grep -fF listA listB > answer

Here are three simple methods using R. Thomas Girke has a lot of useful R stuff. FInd it and use it.

# generate two random lists
a <- sample(LETTERS,20)
b <- sample(LETTERS,20)

# grab Thomas Girke's Venn Diagram functions
source("http://faculty.ucr.edu/~tgirke/Documents/R_BioCond/My_R_Scripts/vennDia.R")

# draw a diagram
qlist <- venndiagram(x=a, y=b, unique=T, title="2-Way Venn Diagram", labels=c("Sample1", "Sample2")
                     ,plot=T, lines=c(2,3), lcol=c(2,3), lwd=3, cex=1.3, type="2")

You'll find that qlist is a list containing the elements of each Venn diagram region. e.g.

> qlist$q1
 [1] "M" "J" "F" "U" "O" "K" "S" "T" "G" "Q" "Y" "Z" "L" "W" "A"

However, if you just need simple counts, you can use the %in% operator:

# count the common elements of a and b
sum(a %in% b)

# get the elements themselves
a[a %in% b]

# or use other functions for sets
intersect(a,b)
length(intersect(a,b))

Note: if you examine the code at the URL above (just load it into your browser) he says he has replaced that Venn Diagram function with something better. Might be worth examining.

R package: VennDiagram

Check this Biostar post for more info.