Your question is really difficult to answer because what you are asking is so open ended. The map you are showing has several different elements that you will need to understand how to work with:
- the map itself has an aerial background or 'imagery' and overlaid on that are point locations - those would be a layer that comes from a feature class that lives in a geodatabase of some sort or as a standalone shapefile. Additionally, there are labels on the map that you would normally create using the label properties of a layer in your map.
- in the upper left and lower right corners are 'inset maps' that show a specific portion of the main map - these would be different maps that are referenced through map frames in the layout to control their display extent and other properties.
- surrounding the main map are a coordinates that are a property of the map frame called a 'graticule' - this one shows the latitude and longitude coordinates but there are other forms of 'grids' that can be shown and have a lot of properties to set that control how frequently the coordinates display, the format of the coordinates, and aspects of the graphical properties like the hash marks and the line weight and color of the 'neat line' surrounding the map.
Essentially you have to figure out how to work with layers in maps that are presented in a layout for outputting as either hardcopy (printed to paper) or soft copy like a .jpg or .pdf. All of these things have a whole host of properties to manipulate to display what you want. You will want to spend some time in the learning resources or help pages - you could start by searching for the various terms I've put in bold text. Welcome to the fabulous world of GIS.
