Recommended mapping tools

You can use any mapping program you like, but here are our favorites:

Google Fusion Tables
You can make simple maps, including different-colored points and shapes with info windows, with Google Fusion Tables. I have a simple tutorial here.
Carto
Carto maps look really sleek and modern, plus you can do some cool animations with them. Carto has great documentation (click on Resources → Documentation). I also have a simple tutorial here, and Albert Kochaphum has provided you a much more full tutorial here.
Palladio
One cool thing about Palladio is that you can make point-to-point maps — meaning, you can show the origin and destination point of one record. You can also import historical basemaps and filter your data in really cool ways. I have a simple tutorial here. The only issue is, Palladio maps aren’t embeddable. You can download them as static images, but your users won’t be able to interact with them.
Esri Story Maps
Story Maps are simple and fun to make. They’re a good choice if, rather than mapping a lot of points, you want to “walk” your viewers through a map-based story. Sorry, I didn’t make a tutorial, but the Story Maps site has great documentation!
StoryMapJS
What?? There’s Story Maps and StoryMap? Yep, sorry, and they’re two different platforms! This one takes a different approach from any of the other platforms: Your “canvas” is one big map, and you click an arrow to advance through all the different points on the map as a story unfolds. I didn’t make a tutorial for this one, either, but the program is really simple and walks you through the process as you go.
GeoJSON.io
Great platform that allows you to create geospatial data and take it into other platforms, like Carto and ArcGIS.