My method is to have a companion with you so as to distract the dragon, then I go straight for the sweet spot. While your companion is is infront of the dragon you come in from the side and attack, stand right next to the hind leg/hip it seems like the dragon cannot hit you with it's tail and it has a hard time snapping at you through it's wing. If you do come at it from the front, you best tactic is to rush it before it can blow it's breath at you and like was said in a earlier post wack it in the nose with your shield like you would a dog with a newspaper and hack away,but be sure to time your shield bashes right so as not to drain your stamina. I'm wearing clothing and this tactic works pretty effectively as long as your companion holds up his/her end of the deal.

Summon Apocalypse, hide in cave! To melee with a dragon is to invite it to bite off your head!

Pretty much this.
I found it harder to battle dragons with my Argonian mage. Mages are very squishy, and takes tons of damage. My two handed warrior Orc, can kill a dragon easily in under 20 seconds.(If it's on the ground)

Just get the dragon to land, pop a potion of fire or frost resistance, and attack from the side of the dragon.

I play a pure melee character that dual wields swords and doesn't block at all.

When the dragon lands, I just power attack the crap out of it. I lose a lot of health, but it loses even more. You need to make sure you have a lot of health. If this is troublesome in the beginning, carry a bunch of potions.

Early in the game I had trouble with frost dragons because they would shoot at you from above and there was no way for me to avoid the damage.

Become Ethereal shout is good for Melee characters while waiting for a dragon to land, maybe try hitting them with a Marked for Death shout first for good measure.

I find attacking side on to be the best option, head on they can bite and tail on they can flatten you with their tails although they can strike out with thier wings as well but not very often.
Dual weild can be a bit risky, but single or two handed using a block hit then following up with two weapon strikes and repeating until dead does the trick.

my melee Nord usually goes straight for the head, shield bash him when he trys biting or shouting at you and keep up the pressure with you weapon, you will be collecting another soul in no time.

Blocking with shields is nearly useless unless you have enchantments and or high block skill.

as liquidpinky said- lol, great name

marked for death is my first shout. and, don't forget to use the appropriate shouts when the cooldown is over.

I've never been picked up and shaken by a dragon, seen it in trailers, i just assumed it was modded, im a melee, but i block alot and attack from the sides.

There is a certain daedric shield that works very well against a dragon's breath.

Never been eaten, just chewed up and spit out.

I generally try to attack the tail and let whoever else is around worry about the head.

I'm kind of a gutless excuse for a "Dragon Born".