From memory:

  • Log in as root.

  • Download the kernel sources from kernel.org and uncompress them to /usr/src/.

  • Open a shell in the directory you just unpacked and run:

    make oldconfig && \
    make xconfig && \
    make && \
    make modules && \
    make install && \
    make modules_install
    
  • Edit your grub configuration and reboot.

If you're not running X then change make xconfig to make menuconfig or make config.

If you want things to go a bit quicker, change make to make -j4 to run 4 tasks in parallel (change 4 to the number of cores your machine has). The same applies to the make modules command.