In general your can take your distros config.
$ cd /home/user/linux/kernel/
(assumes you've already gotten and extracted the kernel sources to said location)
$ make mrproper
$ cp /boot/config /home/user/linux/kernel/.config
$ make oldconfig
(push enter a lot for defaults. Prompted for changes in the new kernel)
$ make menuconfig
(or make xconfig, mostly to verify your preferences. Or to target your specific CPU for compatibility and that 1% performance gain)
And then the usual build stuff. Various distro specific ways to keep your package management system in play. Package kernel-package for make-kpkg which is old way. Using make deb-pkg is the new way in debian based systems. Be prepared for it to take a long time and chew up a lot of space (10G's?).
$ make deb-pkg
$ cd ../
$ sudo dpkg -i whatever_got_generated*.deb
Ubuntu tends to have all the same tools as debian so it should work over there too. Otherwise follow the instructions included in the kernel sources. And reference the ./doc/ tree for further insight. It's not something one needs to do much these days unless you're using bleeding edge hardware. Or deal in the kernel development paradigm.
Be prepared to install things you might not have installed. Especially if you didn't apt-get install build-essential devscripts kernel-package when you built up your current install. Having apt-file installed helps to find the packages you might be missing when you get an error. Instead of blindly installing everything until it magically works.