Where
To enchant an item you need to get an enchantment chips equal to the lvl of the item you wish to upgrade. You can either kill many monsters until they drop the chip you need or get them from a chip exchanger. Monsters will only drop the chips equal to or less than their own level. (i.e. a level 32 monster can not drop a level 40 chip).
You can trade in 3 magic or rare items (blue or yellow) to the chip exchanger, however the chip you get back can't be higher than the items you turned in and is somewhat random. There are chip exchangers located in City of Auch (I-6) and by the entrance to Gigante Beach at Gigante Dock.


Once you have the chip you then bring it to the Enchant girl located City of Auch (I-6).
What
Enchanting can be applied to any item level 32 and above, except uniques.

Result
Results can be any normal modifier found on standard magic/rare items. They can range between just 1 mod, up to 5 mods. Sometimes the enchantment fails, you do lose any stats preexisting modifiers on the item and the chip, but the item is not destroyed.

The following are possible mods for the specific item types:

Leather armor / metal armor / robe / coat
Def + 5 - 20
Evasion + 5 - 15
Movement speed + 5 - 20%
HP +5 - 25%
DR +1 - 3

Shield
Def +3 - 5
Block +5 - 10
DR +1 - 2

Melee Weapon
+5 - 40% attack
+5 - 30% speed
+5 - 10 critical
+10 - 50 psycho/mental
AR +1 - 3

Firearms
+5 - 40% attack
+5 - 30% speed
+5 - 10 critical
+10 - 20 ACC
+30 - 50 psycho/mental
AR +1 - 3

Bracelet
+25 - 40% attack
+15 - 30% speed
SP +15 - 25%
+30 - 80 elemental damage
AR +1 - 3

Canon
+25 - 40 attack
+15 - 30% speed
SP +15 - 25%
+30 - 80 psycho/mental
AR +1 - 3

Suggestions
Take a few plain items (about 20) Upgrade them by doing them in waves (get them all to +4, then all to +5, then all to +6, etc) I've done this up to +8. Then take it over and enchant it till you get the mods you want on it.

Note: An Enchant Booster from the cash shop may be used to greatly increase the chance of an upgrade succeeding.