Remember that, in Mystery Dungeon, evolving has little, if any, impact on the Pokémon's stats; do not feel obligated to evolve your Pokémon if you'd rather keep them in their unevolved forms (like me ;P). Also, the process of evolution will be clearly explained by the game when evolution first becomes possible; you cannot miss the in-game explanation, so don't worry about it for now. If you just started playing the game, it will probably be quite a long time (depending on how quickly you play) before evolution will become possible; in the meantime, there are plenty of interesting unevolved Pokémon to seek out and recruit. ^_^
There is one aspect of evolution, however, that tends to throw people off. If you take a Pokémon to evolve, you will be prompted to select up to two items, if you wish, to use for evolution. For most Pokémon, you should not use any items. The only time you need to use an item for evolution is if the Pokémon evolves in an unconventional manner, such as with the aid of an evolutionary stone; in such a case, select the evolution item to use for evolution and the process will work.
For Pokémon who evolve through happiness in the main Pokémon games (such as Diamond and Pearl), a slightly different process is in order, as the happiness stat does not exist in Mystery Dungeon. Instead, boost the Pokémon's Dungeon IQ with Gummis (Honey also works well in Mystery Dungeon 2) until the "evolution" title on the Pokémon's status screen says "possible" instead of "not now"; typically, four to six Dungeon IQ stars will suffice, depending on the species of the Pokémon.