Cleaning your gutters is easy, as long as you have a long enough and sturdy enough ladder, properly set, so that you can get up to the gutters to see what is in them. Wear gloves so you don't cut yourself. Reach on in and pull out the leaves and other debris and through it down to the ground below.
For the clogged downspouts, you can get what is called a "plumbing snake" from your local Lowes, Home Depot or hardware store, of sufficient length to allow you to insert it into the top, then push it down through the downspout. Be careful you don't hit any electrical wires or anything else that can hurt you. I have a 50' long snake that is really just a stiff, but coiling length of fairly stiff steel that I have used to clear out downspouts over 20' long, and into the underground drainage pipes and it works great. Cheap, too. Be careful!