Help needed: Updating Linux kernel on BBB

I have successfully installed my favourite Linux distro CRUX' on a BBB, which I use as a file and http server. Now I want to update the kernel. I compiled it, but apparently some additional steps are required. Unfortunately, the u-boot’ loader is a mystery to me. Can anybody show me which additional actions I need, or point me to a concise documentation? What I have so far is the zImage and these files:

uEnv.txt on SD-card

mmcroot=/dev/mmcblk1p2 ro

uEnv.txt on flash drive


Greetings, and thanks in advance,