How do I get minecraft capes for free?

To my knowledge only Mojang can distribute the "official capes", that all players can see. You can get them at MineCon, or by making two mini-game maps, and uploading them to Minecraft Realms.

There are also "non-official" capes you can get through mods, that can only be seen by others who use that mod. Optifine has capes, but they are not free. There are, however, mods available where capes are free.

For the majority of official capes, they are only distributed at the discretion of Mojang, mostly for attending events such as Minecon, or making a significant contribution to the game that Mojang has officially adopted, such as MrMessiah's better lighting cape, the Mojira Moderator cape or the Translator cape.

You can get a free official Cape with the migration from your Mojang account to a Microsoft account.

How to get the Cape:
All you need to do is migrate your old Mojang account to a Microsoft account and the Cape will be added to your account. The Cape can be seen by every Player once you equipped it.

To equip the cape once acquired, you have to log into Minecraft.net with your new Microsoft account credentials and at the bottom of the skin selection page will be the cape selection. Simply select the cape and press save.

Everything you need to know about migrating your account and getting a free Cape can be found here.