Most pokemon evolve on their own when they reach a certain level.  However, some pokemon have special needs.  Some pokemon only evolve with stones, some through trading, and some should not be allowed to evolve even though they will try to.  Some pokemon learn certain attacks at a specific level, so for those it is best to wait until the pokemon learns that attack before allowing to to evolve, or using a stone to evolve it.  For example, Pikachu can be evolved to Raichu any time you use a thunder stone on it, but Pikachu learns its most powerful attack, Thunder, at level 45.  If you evolve it before level 45 it will never learn this attack and it will be a useless pokemon. (Note: PWO normally goes by generation 3 movesets.) Check here before you trade another player to evolve a pokemon.

Stone evolutions

Exposure to an "evolution stone" will evolve some pokemon. Stone evolution topic is covered in another page. Go to this page for more details on evolution stones http://grou.ps/pwo/wiki/21753 .

Trade Evolutions

Graveler->Golem
Kadabra->Alakazam
Haunter ->Gengar
Machoke->Machamp

How to Evolve a certain Pokémon on Trade:

Keep the pokémon you want to evolve at your team and each person exchanges the Pokemon in their 1st Position.
You don't need to trade the pokémon you want to evolve. After a "Sucessful Trade" if your pokemon don't evolutes, walk to the nearest area with Wild Pokemon (do NOT switch Positions in your team) and battle a wild Pokemon. Your pokémon should have the option to evolve afterwards.

Pokemon that can't evolve in PWO

Since PWO for the time being only has up to the 3rd Generation Pokemon...some Pokemon that have evolution stages in the 4th generation cannot evolve in the game yet.  Pokemon using hold items or happiness cannot evolve yet either.

Golbat -> Crobat

Gloom -> Bellossom

Poliwhirl -> king's rock -> Politoed

Slowpoke -> king's rock -> Slowking

Magneton -> Magnezone

Onix -> metal coat -> Steelix

Lickitung -> Lickilicky

Rhydon -> protector -> Rhyperior

Chansey -> Blissey

Tangela -> Tangrowth

Seadra -> dragon scale -> Kingdra

Goldeen -> Seaking (Seaking's data is corrupted)

Scyther -> metal coat -> Scizor

Electabuzz (Uncatchable) -> electirizer -> Electivire

Magmar (Uncatchable) -> magmarizer -> Magmortar

Eevee (Uncatchable) -> Vaporeon (Evolution Stone bug)

Eevee (Uncatchable) -> Flareon (Evolution Stone bug)

Eevee (Uncatchable) -> Espeon

Eevee (Uncatchable) -> Umbreon

Eevee (Uncatchable) -> Leafeon

Eevee (Uncatchable) -> Glaceon

Porygon (Uncatchable) -> up-grade -> Porygon2

Pichu (Uncatchable) -> Pikachu

Cleffa (Uncatchable) -> Clefairy

Igglybuff (Uncatchable) -> Jigglypuff

Togepi (Uncatchable) -> Togetic

Togetic (Uncatchable) -> Togekiss

Aipom -> Ambipom

Yanma -> Yanmega

Murkrow (Uncatchable) -> Honchkrow

Misdreavus (Uncatchable) -> Mismagius

Gligar -> Gliscor

Sneasel -> Weavile

Piloswine -> Mamoswine

Porygon2 (Uncatchable) -> dubious disc -> PorygonZ

Tyrogue (Uncatchable) -> Hitmontop
Tyrogue (Uncatchable) -> Hitmonchan
Tyrogue (Uncatchable) -> Hitmonlee

Wurmple (Uncatchable) -> Silcoon
Wurmple (Uncatchable) -> Cascoon

Nincada (Uncatchable) -> Shedinja

Azurill (Uncatchable) -> Marill

Nosepass (Uncatchable) -> Probopass

Roselia (Uncatchable) -> Roserade

Dusclops (Uncatchable) -> reaper cloth -> Dusknoir

Snorunt (Uncatchable) -> Froslass

Clamperl (Uncatchable) -> deepseatooth -> Huntail

Clamperl (Uncatchable) -> deepseascale -> Gorebys