Orrin,
Can you explain what your app is needing to do? From your description it sounds like you want to draw some dots on a map. Where do you intend the data for these dots to come from?
There are lots of ways of doing this depending on your workflow. Are you for example collecting data and do you want to store it somewhere?
We've got solutions but I need to know a little more about what you are trying to achieve.
If you are literally wanting to draw your own dots on a map and you are going to control the location of these through your own app logic, then Graphics Overlays may be a good solution. There are good documents about these:
Add graphics overlays to your app—ArcGIS Runtime SDK for Android | ArcGIS for Developers
Add graphics and text to graphics overlays—ArcGIS Runtime SDK for Android | ArcGIS for Developers
And if you wanted to see a working app doing something similar there are plenty of samples in a git repository. This one shows the use of graphics overlays:
arcgis-runtime-samples-android/java/add-graphics-with-symbols at master · Esri/arcgis-runtime-sample...
The sample above is a Java sample, but the same sample exists for Kotlin too.
Does this help? If this doesn't achieve what you want, then can you explain exactly what you need?
Mark