How do I clean gutters?
I have cleaned gutters at multiple one-story houses by kneeling down from the roof, but I wouldn't risk it on a two-story house.

If you have a two-story house or are wary of cleaning the gutters from a one-story roof, then you have two options: 


As BMitch has said, get a stabilizer bar (~$25-75; I recommend this
one as it is easy to adjust and has no nuts and bolts that you
can accidentally misplace) and an extension ladder (if you are a bit
on the heavy side, get fiberglass; fiberglass ladders are heavier
but stronger.)  This will make your ladder more stable, as ladders
can very easily slide along the gutters, leading to a fall.  Despite
this additional stability, you should avoid becoming too confident
and leaning over instead of getting down and moving the ladder. 
Remember to slope the ladder correctly.  The easiest way to get this
right is to put your toes against each foot of the ladder and put
your hands out, straight forward.  You should be able to touch the
ladder, but just barely.  When moving a ladder that's already set
upon the roof, it's easiest to stand underneath it, between the base
of the ladder and the house.  This keeps the ladder's center of
gravity above you.  Watch how this fireman lifts the ladder,
starting at 2:56.  Pause the video at 3:01 and imagine that the
building is behind him, and all he would do to move the ladder at
that point is to take a few steps to the side and place it back
down.
Another option is to remove the material from the roof, wearing a
harness for fall protection.  You will need a harness, lanyard,
rope, and something to attach the rope to.  You can get all of this
for $100-200.  (Example)  Make sure you wear the leg straps
pretty tight, as they can slide up into and damage your thingamajoo
if you fall when they're loose.


As far as what tools to use, whatever gets the job done.  Hands (gloves recommended), small hand shovel, or maybe something like this.  A broom will also work.  If you're working from a ladder, you should reach for a tool with a short handle.  If you're working from the roof, you should get something with a long handle.  If there's any sand/dirt buildup in the gutters, hit it with the garden hose.