WORK IN PROGRESS
Post questions in this thread and they will get answered. I would prefer to not put any spoilers in this thread so if you have a specific question relating to a quest it may be a better option to create a new thread (if you can not find it posted elsewhere of course).
Please be aware that the information in this thread is only correct to the best of my knowledge at the time of writing. If you see something is wrong please let me know so I can fix it.
Please check the following link for some great guides and info on alchemy, marriage, followers, skill books, dragon shouts and skill leveling, but please note, there may be spoilers;
Before we start, I know there is a lot of writing in this thread, but if you have the time, have a read through these first few posts. Also if you have time have a quick browse through the "Help" menu in the systems tab of the journal in-game. A lot of helpful information can be here and in the in-game help menu and even if you think you are an Elder Scrolls veteran you may learn something new!
The information I have posted in this thread comes from a combination of the following;
There are 18 Skills in Skyrim, which can be broken down into three schools, Magic, Combat and Stealth. Each skill is represented by a constellation. Please note that the following skill descriptions have been taken directly from the Elder Scrolls V: Skyrim Official Game Guide. The black italic text is what is required to actually level up in the skill. They are as follows;
Alteration: Alteration Spells manipulate the physical world and its natural properties. This school includes some of the best defensive spells available (the 'Flesh' spells), as well as a wide range of utility spells like Waterbreathing, Telekenesis and Paralysis. Your Alteration skill increases when you cast a useful Alteration spell on a valid target. For example, you don't get credit for casting Oakflesh but never entering combat, casting Waterbreathing but never entering the water or Detect Life if noone is around.
Conjuration: Conjuration Spells allow you to raise the dead, summon creatures from Oblivion, Draw powerful bound weapons from thin air and trap the souls of your defeated foes. Your Conjuration skill increases when you cast a Conjuration spell and use it effectively, such as sending your summoned creature into battle, doing damage with a bound weapon, or successfully trapping a soul.
Originally Posted by DEG23
The conjuration skill only increases when you first cast a bound weapon spell, if you continue to use the bound weapon it then falls under the weapon category, eg casting a bound sword in combat will raise you conjuration skill, then using the sword on enemies will raise your one-handed skill. Also soul trap only needs to sucessfully hit the enemy to raise the skill, you don't need to sucessfully trap the soul by killing them.
Destruction: Destruction magic harnesses the elemental forces of fire, frost, and shock to obliterate your foes. This skill improves when you damage enemies with Destruction spells, based on the amount of Damage you do. You get the same increase for killing a Frost Troll with one Fire Storm as for killing it with ten Lightning Bolts, and no increase at all if the spell misses it's target.
In addition to its listed damage, each element has its own innate effect: Flame spells set your enemies on fire (doing damage over time), Frost spells slow your foes and sap their stamina, and Shock spells drain their Magika.
Enchanting: Enchanting Allows you to enchant your own magic arms and armor. Your Enchanting Skill increases whenever you enchant or disenchant an item (Based on the value of the enchantment), and when you recharge an enchanted item.
While initially more difficult to level than Smithing or Alchemy, Enchanting is especially powerful in allowing you to maximise your potential with the right combination of enchantments. If you plan to explore Enchanting later in your adventure, it's worth disenchanting the magic items you find early on to build up your enchanting skill and learn a wide variety of effects. You may also want to develop your Smithing skill to ensure you have a ready supply of weapons and armor to work with.
Illusion: Illusion Magic manipulates the minds of those around you, sending them into a Frenzy or compelling them to Flee in terror. Illusion also offers a number of useful spells for a stealthy character, such as Invisibility and Muffle. Your Illusion skill increases when you cast a useful Illusion spell on a valid target. For example you don't get credit for casting Fear on a character that's immune to the spell, or Invisibility when noone is around to see you.
Many Illusion Perks are designed to help you overcome the major limitation of Illusion Magic: the level restrictions on who your spells can affect.
Restoration: Restoration spells shape life energy, allowing you to heal yourself and your companions, drive back the undead, and create Protective wards. Your Restoration skill increases when you use these spells effectively: To Heal damage, turn Undead, or sheild yourself in Combat. It does not increase if you Heal someone who is already at full health, or cast a turn undead spell when no undead are around.