This entire tutorial is only applicable for the Google Nexus 5. Any other phone will not work correctly. Additionally, you really need a Linux distribution to do this (preferable Debian or Ubuntu).
It is really pointless to detail all of the intricacies of building the kernel when CyanogenMod has done such a good job. Follow this tutorial to the letter and you will have built Cyanogenmod. This process will have created a zip file, which contains the CyanogenMod operating system. If you cd to the $OUT directory, like the tutorial explains, you will find it. To actually download the operating system onto the phone, follow this tutorial. The 'Installing CyanogenMod from recovery' section is what you care about. Once you have completed this, your phone is ready for a custom kernel!
To download the new kernel, there are some slight changes from building the whole operating system. Follow this tutorial to build the kernel. After you have completed this process once successfully, I recommend writing a script to do it. It is lengthy and you will have to do it hundreds of times to make kernel modifications. Here is the script I wrote: (just replace [rootdirectory] with your root directory).
cd [rootdirectory]/android/system
source build/envsetup.sh
breakfast hammerhead
mka bootimage
adb reboot bootloader
sleep 10
fastboot boot [rootdirectory]/android/system/out/target/product/hammerhead/boot.img
Now that you have successfully build CyanogenMod and the kernel, you are ready to start making kernel modifications. If you aren't familiar with C, try reading up a bit before you start trying to read the capacitance values.