Two-three years back, installing new kernel and booting from it, is not that easy as you have to update GRUB or LILO with new entry then update grub again to reflect these changes.
But nowdays this has been simplified by just running make command. You can download latest stable kernel from kernel.org. Depending your architecture select kernel configurations or use default config. Then it is just matter of running make and make install. Install target will take of updating your loader. You have to just reboot your system to boot from new kernel.