First, open your Loomso that you have a Loom menu that looks like this: There are 3 slots in the Loom menu so that you can add a banner, a dye and an optional banner pattern.

Complete the first pattern by placing 1 white banner and 1 black dye in the loom and then selecting the Bend option from the list of patterns available (use the scroll bar to see all of the pattern options): This will add the Black Bend pattern to the white banner. Move the completed banner to your inventory.

Next, complete the second pattern by placing the banner from Step #2 and 1 black dyein the loom and then selecting the Chief option from the list of patterns available: This will add the Black Chief pattern to the banner. Move the completed banner to your inventory.

Next, complete the third pattern by placing the banner from Step #3 and 1 black dyein the loom and then selecting the Base option from the list of patterns available: This will add the Black Base pattern to the banner. Move the completed banner to your inventory.