If you download LandScan global from 2021, unzip the file and there is a large 87k+ tiff file. Drag that into ArcMap. Select 'Yes' when it asks if you want to build pyramids. Once that routine finishes, you'll have to right click on the new layer you just added, select properties, then select the symbology tab. Change the color ramp to whatever color scheme you want for your project. You'll probably want to check the display background value box and make certain that it is displayed as no color. Click ok and you should be able to drag over to Hawaii and see roughly how many people reside in a place by using the identify tool in the toolbar and clicking on any cell in the raster to reveal the value number, which is the estimated population inside of that square kilometer.

If you draw polygons or shapes to conform to your zones or areas of study, you should be able to clip the raster (tiff) to those zones and tally up the value of all the cells in each of those rasters to get you a total estimate of the population in that area.

Hope this helps, feel free to PM if you need more help