first the warning
Changing the kernel is not to be taken lightly - you can leave yourself with serious graphics issues and other issues - and even non booting scenarios.
It is wise to disk-image with a good imaging tool such as Clonezilla BEFORE you start.
mainline kernels vs ubuntu stock kernels
The mainline kernels are built using an older toolchain than stock ubuntu kernels. Its perhaps better to consider downloading ubuntu kernels from specific Ubuntu versions
For example - 2.6.38 for Natty, 2.6.35 for Maverick and 2.6.32 for Lucid.
However, you could look forward to v3.2 that is going to be used in Precise - some have reported good power-management issues with this kernel as well as the latest drivers.
There is a similar question here that will give you some further information: How to downgrade the Kernel on 11.10
Assuming your main issue is power-management, then before you consider changing your kernel - consider installing Jupiter - this is an excellent power-management tool.
installing from the mainline
If you must download from the mainline then the full instructions are on the community wiki. In summary 32bit or 64bit deb packages for headers & generic image together with a common "all" deb package.
All .deb packages can be installed with the same syntax:
sudo dpkg -i [package_name].deb
If you want to use 2.6.37 - then just use the latest 2.6.37.x version. Note - none of these kernels will be receiving security updates - you will need to patch these yourself.
If you are using proprietary drivers (e.g. nvidia or fglrx) then you will need to reinstall those drivers. It may be wise to rename your /etc/X11/xorg.conf file first before booting.
There is no way to swap out two complete Kernels. I'm sure you can understand the significance of a monolithic kernel like Linux and why that makes it impossible to simply replace.
The closest you can get is a live-patching process using Ksplice. It converts Kernel updates into magical shims that can plug holes in a running Kernel, allowing you to keep the computer on indefinitely without needing a reboot. For your purposes, it also lets you roll back changes.
It is free for Ubuntu Desktop editions so you can play around with it but you have to pay a subscription for servers (where this sort of thing is most needed).
Just seen your edit. Ksplice probably isn't going to help if you're manually hacking and building your own Kernels for debugging as "the service" is that they provide the special updates and they're not something you can generate on your own.
If you're just building things against an official kernel, it might still work.
One more idea: Virtualisation. You could build your new kernel and swap things around in your VM and reboot. It's still going to take the time it needs to reboot but you could make the VM much more light than your development machine (base it on Ubuntu Server, drop the X server if you don't need it, etc).
Best Answer
If you look at the answers to this question, it may provide some pointers: How do I install an older 2.6.37 Kernel Version?
As far as I can work out, if you go into the Grub menu at start up, just after the BIOS screen, you then have a number of options for booting.
If your Grub menu does not show when you boot up, then the simplest way to display your Grub is to press and hold the SHIFT button while booting.
As an alternative, you can always displays Grub without it booting any particular kernel:
change
grub_timeoutto -1finish off by running