How do I set up districts in Cities: Skylines on the PS4

Solution 1:

Since you mentioned you're on the original game, I take it that you're not talking about the Industries DLC districts (if they are even out for PS4), but rather the base game industry specializations - forestry, agriculture, oil, and ore.

You don't "draw" these types of industry districts, you apply these specializations to an existing district.

So the first step is to just draw a regular district with the district tool. After drawing the district, change to the industrial section. Select the desired industry you want to apply, then target the district you want to apply that specialization to and press the apply button (X?).

Solution 2:

According to the Cities Skylines wiki:

To create a district, click the Districts button located to the right of the zoning button. There, the player has 3 choices of brush size, and simply has to draw the district over the area they wish to cover by left clicking. The brush auto-snaps to roads and intersections, meaning that drawing individual blocks is relatively easy. To remove what has been drawn, simply right click and draw to erase. To expand the size of a district that has already been drawn, hover the brush inside the district until it is highlighted, then click and begin drawing.

Since I've only played the game on PC, I assume that you can use X to draw over the areas you'd like to add to the district.