Basically you just need to copy the running instance to am EBS volume. Before doing this stop any services which change things on the filesystem (mysql, etc...)
So create a volume, make sure it's in the same availability zone as your s3 backed instance, and attach it to that instance.
ec2-create-volume -s 10 -z us-east-1d
ec2-attach-volume -i i-instance_id -d /dev/sdh
Copy everything over to the ebs volume and validate.
dd bs=65536 if=/dev/sda1 of=/dev/sdh
fsck /dev/sdh
Then mount the drive
mkdir -p 000 /ebs
mount /dev/sdh /ebs
make sure /ebs/etc/fstab wont try and mount anything that's not there, then unmount the drive
umount /dev/sdh
You can then create a snapshot of that volume, then you can ec2-register it as an ami, you have to do this from the command line, I don't think you can register an ami from a snapshot using the web interface.
An AMI, as you note, is a machine image. It's a total snapshot of a system stored as an image that can be launched as an instance. We'll get back to AMIs in a second.
Lets look at EBS. Your other two items are sub-items of this. EBS is a virtual block device. You can think of it as a hard drive, although it's really a bunch of software magic to link into another kind of storage device but make it look like a hard drive to an instance.
EBS is just the name for the whole service. Inside of EBS you have what are called volumes. These are the "unit" amazon is selling you. You create a volume and they allocate you X number of gigabytes and you use it like a hard drive that you can plug into any of your running computers (instances). Volumes can either be created blank or from a snapshot copy of previous volume, which brings us to the next topic.
Snapshots are ... well ... snapshots of volumes: an exact capture of what a volume looked like at a particular moment in time, including all its data. You could have a volume, attach it to your instance, fill it up with stuff, then snapshot it, but keep using it. The volume contents would keep changing as you used it as a file system but the snapshot would be frozen in time. You could create a new volume using this snapshot as a base. The new volume would look exactly like your first disk did when you took the snapshot. You could start using the new volume in place of the old one to roll-back your data, or maybe attach the same data set to a second machine. You can keep taking snapshots of volumes at any point in time. It's like a freeze-frame instance backup that can then easy be made into a new live disk (volume) whenever you need it.
So volumes can be based on new blank space or on a snapshot. Got that? Volumes can be attached and detached from any instances, but only connected to one instance at a time, just like the physical disk that they are a virtual abstraction of.
Now back to AMIs. These are tricky because there are two types. One creates an ephemeral instances where the root files system looks like a drive to the computer but actually sits in memory somewhere and vaporizes the minute it stops being used. The other kind is called an EBS backed instance. This means that when your instances loads up, it loads its root file system onto a new EBS volume, basically layering the EC2 virtual machine technology on top of their EBS technology. A regular EBS volume is something that sits next to EC2 and can be attached, but an EBS backed instance also IS a volume itself.
A regular AMI is just a big chunk of data that gets loaded up as a machine. An EBS backed AMI will get loaded up onto an EBS volume, so you can shut it down and it will start back up from where you left off just like a real disk would.
Now put it all together. If an instance is EBS backed, you can also snapshot it. Basically this does exactly what a regular snapshot would ... a freeze frame of the root disk of your computer at a moment in time. In practice, it does two things different. One is it shuts down your instance so that you get a copy of the disk as it would look to an OFF computer, not an ON one. This makes it easier to boot up :) So when you snapshot an instance, it shuts it down, takes the disk picture, then starts up again. Secondly, it saves that images as an AMI instead of as a regular disk snapshot. Basically it's a bootable snapshot of a volume.
Best Answer
EBS volumes can be attached and detached from EC2 instance.
If you have an EC2 instance that crashes for some reason, you can move the root volume to another EC2 intance.
Technically, it can be done.
However, you may encounter the same problem that you had with the original EC2 instance since you're booting from the original root volume.
Another thing you can do is to attach the original root volume as a non-root volume on your new EC2 instance, such as /dev/sdb1. If you do this, you can examine the data on the volume to determine the cause of the crash and perhaps fix it.
One more thing, while you can make an AMI image out of an EBS snapshot, you can also make AMI images directly from the EC2 instance instead. As a process, this often is simpler.