If there is a configure file also, The usual pattern, in a terminal, is;
./configure
make
su
root password
make install
If there is no configure file in the directory, then;
make
su
root password
make install
Usually there is a
README file, and possibly an
INSTALL file, that are plain
text files, that give instructions on installing the application/driver.
When I do a search for Realtek drivers for that kernel, I get this.
[root@fatman ~]# locate rtl81 |grep 2.6.27.31.tex5/lib/modules/2.6.27.31.tex5/kernel/drivers/net/usb/rtl8150.ko.gz
/lib/modules/2.6.27.31.tex5/kernel/drivers/net/wireless/rtl8180.ko.gz
/lib/modules/2.6.27.31.tex5/kernel/drivers/net/wireless/rtl8187.ko.gz
Have you tried any of these?