Install VMware Tools on a Linux Client

First, log in to the VM as root and "yum update".
Then "yum install gcc make binutils kernel-devel kernel-headers".
Then reboot the VM.
Then start up the vSphere Client, right click on the VM and choose Guest - Install VMware Tools.
Back into the VM's root session.
mount /dev/cdrom /mnt
cd /tmp
tar xzf /mnt/VM*
umount /mnt
cd vmware-tools-distrib
Accept all the defaults, and let it do everything it wants. If you have a fully updated and correct system, it should install flawlessly.

Check the "ifconfig -a" and ensure that all the network devices that exist have startup scripts in /etc/sysconfig/network-scripts/ifcfg-eth*.

Go into the vSphere Client again and right-click on the VM. Look in the "Guest" sub-menu and tell it to stop installing the VMware Tools if it offers you that.

Reboot the VM.

If you have problems...

The most likely problem is that you are running an el5xen kernel or some other xen kernel, which you don't want to be doing.
Once you've done a yum update, take the xen kernel you are running (uname -a will tell you) and do something like this:
yum install kernel-2.6.18-164.el5
Then edit /boot/grub/grub.conf and ensure that the "default=" setting at the top is set to boot the kernel you just installed and not the xen kernel (they start numbering from the top of the file from 0).
Then reboot so you are running the non-xen kernel.
yum install kernel-devel-2.6.18-164.el5
Then re-run /tmp/vmware-tools-distrib/ and if it asks you for the kernel headers location, give it
But you will most likely find that it just happily works on its own!
Then just reboot to pick up all the VMware tools in a fresh boot.