Loading a map in desktop GIS software is simple. If you go in the administration menu on Maps and click one of the maps, you will see on the new page a map and few generated links. Use the link in the Web map service section. If you have the Free or Vector plan, you need to use a different method to load the map (read below).
In ArcGIS, click on Add Data button and select the first option: Add data…
In the file browser window, select from Look in drop-down menu GIS Servers option.
Now select Add WMTS Server option by double-clicking and paste the generated address into URL bar. To see available maps, click on the Get Layers button. Now confirm by clicking on OKbutton.
Your maps are now be listed in Catalog, to active the map, just drag and drop a map to the Layers menu on the left and your map is ready.
In QGIS, click on Add WMS/WMTS Layer… in the left menu (shortcut Ctrl + Shift + W) or from the context menu select Layer -> Add Layer -> Add WMS/WMTS Layer….
In the new window, click on New, write any Name and paste the generated link into URL bar.
If you now click on Connect, it will guide you to the list of available layers. Select one and click on Add.
If you want to change the layer, open the Add WMS/WMTS Layer… window again, select your layer from the drop-down menu a click on Connect.
ProTip: To improve the look of any WMS/WMTS in QGIS, just right click on the layer in the Layers panel, select Properties and in Styles set the Resampling method for out to Average.
Other GIS software
There is a similar process for MapInfo, gvSIG, GRASS GIS, uDig and other GIS software. If you are interested how-to open map in any of these, search for How-to open WMTS in my-favourite-GIS.
QGIS Vector Tiles Reader plugin
If you have the Free or Vector plan, you can still open our maps in QGIS with a Python plugin for loading vector tiles source with styles. You can install it directly from the plugin manager. The plugin adds you an icon to left panel which allows you to add and vector tiles source.
Add a vector map with styles copying paths from the administration. You need to add a link to TileJSON as a vector tile source from Data section and link to hosted style from its page:
The opened map will be added as a group of layers. Plugin converts a style to QGIS native styles so there is a possible change each layer separately. Labels are converted to native labels too.