UESP wiki has a lot of tips for leveling all skills. In this post I would like to describe the fastest way to level combat skills, namely, one handed, 2-handed and archery.
Combating high level enemies – dragons, briarheart etc are good ways of leveling these skills. However, it is not always easy to find these enemies in abundance. One way to level faster, is to use ‘heal other spell to heal your opponent and use a weapon that does little damage. Bound weapons are a good choice, especially if you don’t have any talents points in Conjuration tree. I used a small iron dagger that did 7 damage, and a bound bow (since I didn’t want to worry about carrying a huge amount of crappy arrows for the sake of leveling). Hitting the enemy and healing them repeatedly is a good method if you need to level restoration as well. However, heal other adds an overhead if restoration is already at 100. Instead, I found that hitting Shadowmere while he tanks the opponent is way faster. Shadowmere has very high health regen, so he would never die or turn on you, unlike a summoned dremora lord, who in my experience turns on you after 4 hits regardless of the damage done.
I find Briarhearts a little too tough for this task. They do a lot of damage and I find myself constantly healing myself and pausing. Hence, I leveled my skills while fighting an ancient dragon. I brought the dragon ‘s health down just enough so that it was permanently grounded and did not fly off for the rest of the battle. I stopped attacking until I was sure that shadowmere was ‘tanking’ the dragon and the dragon would not hit me with my fire breaths. At this stage, I started leveling my combat skills by hitting shadowmere. Using this method, I found that my 1 hand and archery skills leveled 1 skill point every 2-3 minutes from 95-100.
Also, note that for Archery there is a quest at Angi’s Camp south of Falkreath, which gives up to 6 skill levels if you pass all the skill tests. I saved this quest until after I was 90 in Archery, so I had only a few skill points left to level after the quest was complete.