To verify the signature (and import the key in the last step above), you'll need to have GnuPG (http://www.gnupg.org) already installed. See http://www.kernel.org/signature.html for full instructions, but essentially once you've got GnuPG set up and the correct key imported, the command you want to use is:
gpg --verify linux-2.x.y.tar.gz.sign linux-2.x.y.tar.gz
Unless you have taken explicit steps to build a trust path to the Linux Kernel Archives Verification Key, you should expect to see a warning message, which is ok. What you want to look for is something similiar to "Good signature from..."
$ cd /usr/src/linux-2.4.x
$ make mrproper
$ make menuconfig
I would recommend the following, at a minimum:
$ make dep
$ make clean
$ make bzImage
$ cp arch/i386/boot/bzImage /dos/vmlinuz
Suppose you actually want to be able to boot to your new shiny kernel? Forget about LILO; use Loadlin instead. I've had nothing but headaches with LILO as a boot manager. On the other hand, I've never had any issues with LOADLIN. Using Loadlin is simple and effective. The instructions are fairly straight-forward, so I won't go into the details. Make sure to copy your shiny new bzImage file to your dos partition, using DOS 8.3 naming syntax. The source for Loadlin is available at ftp://elserv.ffm.fgan.de/pub/linux/loadlin-1.6/lodlin16.tgz
Here's the two file configurations I use. The first is from CONFIG.SYS:
[menu]
menuitem=linux, Linux
menuitem=single, Linux (single user mode)
menuitem=dos
menucolor=15,1
menudefault=linux, 10
[linux]
[single]
[dos]
And here's the corresponding AUTOEXEC.BAT file:
@echo off
goto %config%
:linux
c:\loadlin.exe c:\vmlinuz root=/dev/sda5 ro
goto dos
:single
c:\loadlin.exe c:\vmlinuz root=/dev/sda5 ro single
:dos