Once you make your new kernel, how do you put it into use? 

Grub is the default boot manager on most new linux distributions. In particular on Debian Sarge. Grub has a simple config normally in: /boot/grub/menu.lst, editting it (kernel boot order is done by order in the file) to add:

title           Debian GNU/Linux, kernel 2.4.27-3-686-smp-BIGMEM
root            (hd0,0)
kernel          /boot/vmlinuz-2.4.27-3-686-smp-BIGMEM root=/dev/md0 ro
initrd          /boot/initrd.img-2.4.27-3-686-smp-BIGMEM
savedefault
boot

You can hand-edit this, or on debian use the update-grub command which does this for you. update-grub likes to have things named in a sane fashion (all parts, config, System.map, initrd, image all named in the same vein):

-rw-r--r--  1 root root   43461 2007-02-23 12:42 config-2.4.27-3-686-smp-BIGMEM
-rw-r--r--  1 root root 4300800 2007-02-23 12:55 initrd.img-2.4.27-3-686-smp-BIGMEM
-rw-r--r--  1 root root  539677 2007-02-23 12:49 System.map-2.4.27-3-686-smp-BIGMEM
-rw-r--r--  1 root root  932493 2007-02-23 12:48 vmlinuz-2.4.27-3-686-smp-BIGMEM

All of these files are copied save the initrd which you can make with:

mkinitrd -o /boot/initrd.img-2.4.27-3-686-smp-BIGMEM

Then reboot and enjoy your new kernelly-goodness.