Oblivion:Fortify Skill

Increase the value of the target's given Skill by M points; the effect lasts for D seconds.  Fortify Skill will improve your ability to use the given skill (e.g., weapon damage will increase; the magicka cost of spells will decrease) as described in more detail at the Skills page.  However, in most cases using Fortify Skill to boost your skill to a new mastery level will not bestow the skill perks of that mastery level.  See Notes for known exceptions.

Internally, all of the various Fortify Skill effects are considered to be the same, so learning Fortify Blade, for example, will give you access to all 21 Fortify Skill commands at the Spellmaking Altar.

When a Fortify Skill effect is active, purchasing training in that skill will be more expensive.  However, Fortify Skill normally has no effect on the rate at which you gain experience in that skill.  For example, if you are level 12 in Conjuration, it takes two spell casts to advance to level 13.  With +10 Fortify Conjuration, it would still take just two spell casts to advance from boosted level 22 to boosted level 23 (whereas four spell casts are necessary once you naturally reach level 22).

The exception to this rule is when the Fortify Skill effect is implemented as an ability. In this case, the skill will advance slower when the ability is active. The most common effect is with the Skeleton Key, but see Fortify Skill Abilities for a complete list.

Notes
Fortifying a skill past 100 does not provide any additional effect. The two exceptions to this are Acrobatics and Athletics. 
As a spell, Fortify Skill is not available from any built-in spells.  There are several other ways to acquire access to this spell effect, however (some of which are described in more detail at Free Skill Boosts).  Obtaining any one of these powers, abilities, or spells (i.e., having it appear in your Magic Menu or Active Effects menu) will grant you access to the Fortify Skill effect for enchanting and spellmaking purposes.
Most Doomstones bestow Greater Powers that include various Fortify Skill effects.  For example, the Apprentice Stone provides the Void Seed power, which fortifies Illusion and Alchemy skills. 
Completing the Origin of the Gray Prince quest provides a constant effect Fortify Skill reward.
Completing the Whodunit? quest for the Dark Brotherhood provides a bonus ability ''Night Mother's Blessing'' with fortify skill effects.
Completing Nocturnal's Daedric quest and acquiring the Skeleton Key makes the Fortify Skill effect available as long as you have the Skeleton Key in your inventory.
Becoming a Vampire gives access to both Fortify Skill and Fortify Attribute effects.
In the official plug-in Thieves Den, the hideout can be upgraded with several vendors who sell spells with various Fortify Skill effects.
In the official plug-in Spell Tomes, several spells are added that provide Fortify Skill effects.
As a potion, this effect is only available in the Strong and Grand Elixirs of Exploration
From Sigil Stones, only Fortify Blade and Fortify Blunt are available.
Although Fortify Alchemy is available as an effect, in most cases it causes no improvement in your Alchemy abilities (the only exception being the Fortify Alchemy effect available from the Altar of Alchemy in Frostcrag Spire).
As discussed in the introduction, generally skill perks do not become available when using Fortify Skill.  The few known exceptions are:
Fortify Acrobatics to 100 will bestow the water jump perk.
Fortify Armorer to 100 will bestow the unbreakable repair hammer perk
 
Although fortifying a skill will not allow you to use spells of higher requirements, you can use fortify skills to create higher level spells at an altar of spell creation. For example, if you want to make a spell that requires 50 restoration but have a skill of only 44, you can fortify your restoration skill by 6 points and the altar will allow you to make it (although you cannot use it yet). The cost of creating spells is also significantly reduced.
Fortifying a skill to 70+ will allow you to do that skill's Master Training quest.
Talking to NPCs while Fortify Skill is in effect will modify the NPC's reaction to you accordingly.  Since time essentially freezes while in conversation, a custom-made Fortify Skill spell (such as Fortify Mercantile) with 100 magnitude and 3 duration could provide useful benefits.

See also
Sections:
Restore vs. Fortify vs. Absorb: A comparison of these similar effects.

Related effects:
Absorb Skill, Drain Skill
Fortify Attribute, Fortify Fatigue, Fortify Health, Fortify Magicka