How do I install the custom ROM with boot.img inside?
Please check the place where you downloaded the ROM from, it usually contains installation instructions. In most cases, these ROMs use the update.zip mechanism of the recovery mode, as Matthew mentioned. You might need a custom recovery (see clockworkmod and twrp and their tag-wikis, clockworkmod resp. twrp, for examples).

The process then usually is as follows:


copy the .zip to your SDCard
boot into recovery-mode
select to "apply update from SDCard"
navigate to and select your .zip
let it flash
go back to the main menu and select to "reboot device"