There is no way to make a cape in "Minecraft" as of 2015. Capes are vanity items awarded to players under rare circumstances. Capes in-game have also been called cloaks in the past, but capes and cloaks are the same item.
One example of a unique in-game cape is Miclee's Bacon Cape, which he received for submitting Pigman as a village mob. Another player, akronman1, received the One Million Cape for buying the one millionth copy of "Minecraft." Cheapsh0t received Cheapsh0t's Cape for his contributions on the Mohjang Tokyo development team in 2013.
As for non-unique capes, real-life attendees of the 2011, 2012, 2013 and 2015 MINECON conferences received Attendees Capes unique to that year. Moderators who contributed to in-game translations were randomly selected to receive the Crowdin Translator Cape. Select moderators who worked on the Chinese translation project received the Chinese Translator Cape.
"Minecraft" players are sometimes awarded temporary capes for in-game events. For instance, all Xbox 360 players received the First Birthday Xbox Cape from May 9 to May 13, 2013. On Christmas Eve and Christmas Day, 2010, all players received the Christmas Tree Cape. These capes were only available on the days of their respective events, and were removed from display after the events ended.
Players can download capes or cloaks as client mods, but these mods are only visible to the player client-side and are not visible when playing online.