Skills

Powers and abilities

Shirou's and Archer's abilities are almost the same, although we can say that Shirou is less powerful, in someways, but it isn't actually that true, since he has only less experience. Since Archer is also a usable servant in the game, I'll also add his general stats followed by the descriptions of skills and general attributes.
You could also find some Archer/Shirou related words and definitions taken from the glossary of dies irae.

Stats

Archer's statistics

standing: True Neutral
strenght: D
endurance: C
agility: C
mana: B
luck:E
noble phantasm: None, but for more info please read the following paragraphs!

Attributes

Archer's general skills

magic resistance: D
indipendent action: B
clairvoyance: C
sorcery: C
eye of the mind (real): B

Abilities

Archer's and Shirou's abilities

imagine: Shirou's ability/magic power to create objects and weapons through his imagination. Imagine is a higher and ultimate form of Tracing (although it has different effects and a higher endurance). Shirou acquires it in Heavens Feel.

reality marble: Shirou's and Archer's condition or magic power to apply tracing to a large scale and perfom Unlimited Blade Works. The reality marble allows them to get an ability that can be compared to a Noble Phantasm (since they haven't any). This particular power creates the Unlimited Blade World.

tracing: Shirou's ability/magic power or skill he aquires in Fate and masters in Unlimited Blade Works. It's the power to create a weapon by copying it by an other weapon. It's not only a matter of material but also knowledge since he can acquire also the memories and abilities of the original owners of those weapons he copied.

unlimited blade works: Shirou's and Archer's Reality Marble that can be associated to a Noble Phantasm. Through the mana accumulated and the tracing ability they can create an unlimited number of swords (again copied swords) and create a connection to the unlimited blade world, a sort ot parallel world representing their own feelings, emotions and fears.

Miscellaneous

Everything else

EMIYA: the transiction between Shirou and Archer, a sort of unworthy person with the desire to become a heroe, who made many mistakes and who was unable to save teh life of those he should protect.

heroe of justice: Shirou's dream to become the reincarnation of the Heroe of Justice in order to preserve people's life and protect everyone; a vane dream that grew in his mind because of the admiration he felt for Kiritsugu, a distortion of reality.

pact with the world: the agreement between Shirou/EMIYA and the Throne of Heroes that allows him to be able to change the destiny of those he killed, by mistake to reach his ideal of justice, and save them. Although he got this miracle he wasn't really able to save everybody with the result that he destroyed more lives than those he saved. In exchange for this blessing he accepted his fate to become an eroic spirit.

throne of heroes: the entity that preserves and collect the spirits of heroes and turns them into heroic spirits. It's developed in a parallelar plane where there isn't any representation or concept of time, that's why any spirit can be transfered to any point of history and space through it (because the concept of time doesn't affect it).