It depends on the costume. For holiday costume items, for holidays like Christmas, Easter, and Halloween, Jagex (the company that runs Runescape) hosts events, which are like mini-quests. When you complete the quest, you are given a piece of a costume.
Some holiday items from past events are available on the Grand Exchange, but for huge sums of Runescape GP (tens of millions)
Other costumes you can earn points for after successfully completing a random event, if you choose the "Save up for outfit!" option after opening the random event gift. When you save up enough points, you can redeem certain costumes (not the ones from holiday events) at Thessalia's Fine Clothes near the center of Varrock.
Still more costumes are given as a reward in Balthazar Beauregard's Big Top Bonanza. The higher your level in either Ranged, Magic, or Agility, the better the costume you are given.
rogue
You obtain Costume Points, by successfully completing Random Events which reward you with a Costume. Then you redeem these points at Thessilia, in Varrock.
Many people believe it does help.
Get the mime random event, and choose the 'costume point', then travel to varrock and go to the clothing store and use your point and pick which piece of the mime costume you want
Not all at once but once you have had enough of the events you will.
Lots of people have different opinions on what best to wear in Runescape, but IMHO I would say that wearing the saradomin robes set with a blue h ween mask and a prayer cape.
The Santa Costume was a Christmas event in 2009 were you helped Santa find his son. For a reward he gives you a Santa costume without the hat. The Santa costumes are untradable but the Santa hat can be bought at the Grand Exchange in Varrock for something like 13 or 14 mil.
If the costume was from a random event, then you will have to go through the long process all over again to get a new pair. If it is from the holiday events (Christmas, Halloween etc.) then you can get replacements from Diango (Dranor Village, Market).
Has no use other than costume. It costs a lot since it's obtained from a level 3 clue scroll.
Wear a random event given costume, if you have a prince set or Wizard set they will do.P.s things may be different this year, this was a Halloween event quest back in 2008, may not happen the same way this times.
Shade Robes provide a small amount of prayer bonus, less than Monk Robes. They're untradeable and can be stored in the costume room.
If it's cheap it isn't awesome, but Mixing Kyatt Hunter Gear with Black Dragon-Hide chaps may seem nice.