Currently, you can't upload data and add it to the web map. The only layers that can be added are services running on ArcGIS Server.
If you have a limited set of points that you could enter manually over the map, you can do so. From the map:
1. Click Add
2. Click Create Editable layer.
3. You can now add points.
We are working on allowing you to display different data types, such as shapefiles and CSV files over the map. Pricing has yet to be determined.
Thanks,
Mike