This should be a fairly self explanatory one. Use a lot of healing spells. Most people will use this quite often anyway since it can get expensive having to constantly buy potions. A quick way to get this up quickly is to find some area in the game, such as a trap that doesn’t get destroyed when you trigger it. Flame traps are usually good as they just keep blowing fire so long as you trigger them. Keep taking damage from the trap and also keep healing yourself as often as you can. Using the one time healing spell rather than the continuous healing spell is the best way to go since you don’t regain magika while you are casting a spell. Step away from the trap if you find you are taking more damage than you can heal. This can also be a great time to increase your light or heavy armor skill.
An alternative method would be to find an NPC that either you damage or someone else damaged, but does not become hostile. It also doesn’t matter if they do become hostile, so long as they can’t easily kill you. Equip a weak sword, or better a weak destruction magic spell. Start attacking them to take health away, this should allow you to raise the skill of your destruction magic or weapon skills. Then use the spell called “Helping Hands” to heal the same person. This lets you kill 2 birds with the one stone. IF they do land a few hits on you, it may also help you raise your defense skills.